In my learning, I'm nearing that point when the notes just seem too fast to be picked individually. Most tabs I come across contain hammer-ons and pull-offs for fast notes. However, I'm finding that by picking each individual note, I can produce better sound and even play more accurately, even if the notes are really fast (by my current definition of fast anyway). I'm wondering if it's "OK" to pick all notes instead? Will this cause problems later on?
Of course you can pick each note separately. But, they'll have a terminal velocity. Think about it - a hammered on note can be literally as quick as banging the next note down, much quicker than recovering your pick or finger. And pull-offs are similar in speed. Try doing consecutive hammers and pulls on, say, 4th and 5th frets. Lightning speed in comparison to picking each note!
But only when they're done properly. Hammer-ons need to be smart and firm, and will eventually sound much like picked notes. Pull-offs will sound exactly like a finger pick, because that's what they are - only with the fretting fingers.
It won't cause problems later, as the more you play, the quicker the picking will get, but learning to produce good sounding hammers and pulls will set you up for great legato playing anyway. Listen to experts and it's almost impossible to tell the difference between those and simple picked notes.
I would say it's not ok.
Obviously, how you play a certain piece and your personal style can differ from one person to another and one song to another. But you asked the question in the context of learning to play the guitar and not in the context of fingering for a certain song.
As you get better, you will not pick as fast as you can hammer on and pull off. Failure to learn the technique will limit your speed a great deal.
As songs get more complicated, you will find that there are times when you want to do a hammer on or pull off when picking it will be exceedingly difficult. In particular, rhythm parts that include a strumming action for the chords and hammer ons or pull offs for accent or melody.
Hammer ons and pull offs are heavily used techniques in guitar. You should take the time to learn them, even if you can "get around it" at your current skill level. That won't hold true as you get better.
It will cause the "problem" that you will have your own sound and playing style.
At some point, most players want to learn hammer-ons and pull-offs. At some other point, most players want to learn to pick every note in a fast run cleanly and fluidly. Usually players learn the legato hammer-on and pull-off style first, since it seems to be easier. There's no need to learn it first. You won't hurt yourself by learning to pick every single note at this time.
Notice I'm assuming you will eventually come back and learn hammer-ons and pull-offs. I'm very confident that sooner or later, you will. If you never do, then you will have firmly fixed your own style and there will be some sounds and styles you won't be able to reproduce. If that's how you turn out, that's ok. There are plenty of excellent guitarists who are unable to execute all kinds of techniques, even basic ones. If you watch Bruce Springsteen carefully, he is a terrible guitarist, from a technique point of view. But he is the only one who plays the way he plays.