Hi Jay,
Yes, with MIDI regions, you can have them overlap and they will both play. And yes, if it's a mater of long regions overlapping for a couple of beats due to a pickup; that's fine. I do that all the time too. But I like putting them onto separate tracks when they are playing at the same time. Completely overlapped regions on the same track are hard to select, see, edit, etc.
For example,let's say I have a piano part playing chords. And also a melody line in the higher range. And I want to double that melody line with strings, or a guitar, or whatever. I'll record the chords on one track. Then do the control - shift - return thing and play in the melody. Now I can easily copy that melody region onto another track. Of easily select only a portion of it - if that's what I need - to copy or move, etc. It makes it easier to edit and also to see - in terms of what is going on in the arrangement.
Or, same scenario, maybe I have two different chord parts on the piano that I want to try; I'm not sure which one will ultimately work better in the arrangement. Control-Shift-Return, record all the alternate parts I want to try, turn the power button off on them to silence them until I am ready to try the alternates.
Or, I am recording in a solo. I want to record several takes and then choose later. I prefer the control - shift - return method than MIDI take folders for this; they're easier to edit. With take folders, you have to split them on to separate tracks to edit them anyway. May as well skip that step!
But yeah, it's certainly unnecessary for a beat or two overlap.