I would like to share my thoughts as they relate to your question about iOS touch to sound latency and "(virtual or MIDI) musical (instrument) practice or performance?"
I must assume that your primary interest is - latency as it relates to iOS musical instruments and devices or other "virtual and digitally produced musical sounds (MIDI) during "practice or performance" on these type devices or "instruments".
For the TL;DR skip to the end. To understand how I arrived at the conclusions at the end - continue reading.
The studies cited in Some Dude's answer and some of the anecdotal information cited in comments - relate to musicians playing real (as opposed to virtual) instruments. But what we learn from these studies and observations will lead us to some logical conclusions as they relate to your specific question.
First let me add to the anecdotal evidence from my perspective as a performing guitarist and vocalist who has also played some keyboard and piano. I often perform in a totally acoustic setting with un-amplified acoustic guitar and no microphone. In a case like that, the latency is very low - particularly on vocals. When I perform plugged in and sing through a mic, I generally use floor wedge monitors fairly close. None of these scenarios pose any problems for me.
When I perform in larger venues with a house PA and monitors that may be suspended from the ceiling, I am quite uncomfortable with the delay between the time I pluck a string on my guitar and the time I hear it through the monitor - and I have a difficult time performing under those conditions. I am sure that if I did that all the time as a matter of practice, I might eventually get used to it and adapt.
So let's look at what we can extrapolate from the AES study shared by Some Dude. Then we can make some conclusions about what the findings might suggest for virtual instruments.
In that study we learn that vocalist and saxophone players have the least amount of tolerance for latency and keyboardist and drummers have the most tolerance and guitar players are in between. The findings of the study clearly show that the tolerance levels are directly related to the instrument and NOT the individuals. The same individual playing different instruments would have latency tolerance levels consistent with other results on the given instrument.
So let's consider why that might be true. Whenever you talk or sing, your brain expects an immediate zero latency response to sound coming out of your mouth at the exact same time your diaphragm and lungs push air over your vocal chords. It has been that way from the time you entered the world screaming and hearing the sound of your own voice for the first time. So it's easy to understand why a vocalist, would have a low tolerance for latency. The brain is used to immediate feedback when vocalizing.
With the saxophone player, the brain has developed a similar expectation. Making a sound with a horn has one very significant cause and effect commonality with making a sound with your voice. The act of blowing air - produces an immediate sound. Whether singing or blowing a horn, there is a very conscious physiologic muscular action that produces a simultaneous and instantaneous reaction. Horn players are used to blowing through their instrument and immediately hearing a sound.
EDIT: Community member Supercat made and excellent point in comments and I felt compelled to include it in this answer. To sing a note with voice or to play a note with many types of horns - the facial muscles and vocal muscles actually control the sound as it's being created and minor adjustments must be made during the creation process to reach the desired pitch. So a singer for example can hear in the monitor if he/she is a bit sharp or flat and immediately make the necessary adjustments to the facial/vocal muscles to correct the pitch. Another good explanation for lower tolerance of latency for a singer or horn player.
Now let's consider why keyboardist have such a high tolerance for latency. Most keyboards including acoustic pianos have a slight delay between the time you press a key and the time you hear a sound. On acoustic piano, pushing the key triggers a mechanical action - which eventually causes a hammer inside the piano to strike the strings. But it is not an immediate "hit it and hear" it effect. Synthesizers and digital and electric piano's have always had some degree of latency. So keyboardist have had to learn to adapt to the unavoidable latency from the moment they began playing. So to a keyboardist, latency is normal and expected - therefore well tolerated. It's what they learned to expect from the very beginning.
With a drummer, it is in fact a hit it and hear it response. So how do we explain a drummer's tolerance to latency in the AES study? The study done in 2007, did not mention the use of electronic drums for testing the drummer's tolerance to latency so I must assume that the drummers in the test, used an acoustic kit.
A drummer hitting an acoustic drum with a drumstick, quite frankly does not need a monitor to hear the sound of his drum. A drummer uses a monitor NOT to hear himself (some drummers even wear earplugs because they can hear their drums TOO well) but to hear the other musicians (and the other musicians turn up their monitors so they can hear themselves over top of the drummer).
So a logical conclusion that we can make based on the results of the AES study - is that tolerance to latency is **learned.** The brain learns all kinds of useful information that keeps us sane. For example, any time your eyes are open, you see your nose, but the brain has learned to disregard that image, because your brain knows it's not important.
The brain has learned to expect immediate feedback when we exert the necessary muscle contractions to blow air - either through a horn or our vocal chords. If we learn to play a piano or other keyboard instrument - the brain LEARNED from the beginning to adjust to the built in latency of the keyboard.
So my expectation would be, that we can easily learn to tolerate latency with most virtual instruments, because we have not been pre-conditioned to expect otherwise. If we never learn to expect an immediate response from virtual instruments, latency should not present the same problem it would for a vocalist, or sax player or guitarist.
I would also expect that with iOS drums played on a touchscreen, latency might very well present some timing issues. If you tap the screen and don't hear an immediate response to the drum, it could make playing in time very difficult. Just the opposite of what live drummers on real acoustic kits experienced in the latency tolerance test.
In reality, there is no tolerance for latency for a drummer. It's impossible to create or simulate latency for a drummer on a live acoustic kit. But on an iOS drum, you could introduce latency - and I would suspect that this would be the one case - where a few milliseconds of latency would matter.
Recording and monitoring vocals is not included in the scope of this answer because you did not mention vocals or even recording (just playing and practicing - instruments) in the question. So that is a completely different discussion.
TL;DR - The bottom line answer to your questions:
Question: "What are the situations where a few milliSeconds of latency really matters?"
Answer: When playing iOS or MIDI drums on a silent pad or touchscreen if playing with other music where timing is important.
Question: "What are the situations where even dozens of milliSeconds of latency might still allow acceptable (virtual or MIDI) musical (instrument) practice or performance?"
Answer: When practicing or performing on any iOS or MIDI or virtual instrument other than drums.