The recommendation from the website referenced by the orignal post is generally good on unisons, for at least a couple of reasons:
When a unison is "close" it becomes a matter of discerning the quality of the sound rather than counting beats. This is difficult to do by simply comparing frequencies on a device because a string is not an electronic oscillator, it typically has an "envelope" of sound which can be best compared by ear.
Sometimes a string will have a "false beat" wherein two (or more!) notes in close frequency proximity are produced by one string. When this happens, it is difficult to know "where" to tune it electronically. The best compromise with the other strings is best determined by ear.
Some professional tuners have reported success with various software packages in tuning each string to a reference and ending up with good unisons. I have tried this with mixed results. I find that focusing on a number and its accuracy diverts attention from the quality of the sound. I will never be perfectly accurate, so how close reaches my goal? I've found I can't tell unless I'm listening, so I always go back to that.
For octaves the above comments apply, and then inharmonicity comes into the equation as others have answered here. Until relatvely recently, "by ear" was the only way to deal with this as well as with the constraints imposed by equal temperament. A chromatic tuner will not be able to accomplish this alone, and that is where the more sophisticated devices and programs come in.
I believe the answer to your second question is "perhaps," depending on how much skill you develop in the aforementioned tasks, and what level of tuning quality you are going for. It may be the case that following those instructions will result in a tuning that is "good enough," and you won't know until you try.
If you're just learning tuning, instead of a chromatic tuner try TuneLab. It's still available in free trial-mode in its older versions and on some devices and operating systems.