Can I just turn the adjustement screws to find the limits in all directions, and then split the difference?
Yes.
I've never turned and adjustment screw all the way and I don't know what happens. Does it [...] come completely unscrewed?
Nope, not unless it's some horridly cheap scope, and even then probably not.
Yeah, what I do is go until you reach one end or the other, one click at a time, until you feel undue pressure. When you do feel that pressure, don't force it obviously. (However, sometimes they are stiff and you think you're at the end when you're not, so you have to apply just the right amount of pressure to figure out if you're at the end). Then start counting and go all the way back to the other end, for the total clicks. Then write this number down in a spreadsheet on your puter. Divide by 2, and count back to the middle. Repeat with elevation (if you did windage first), then bore sight it with both axes in the middle like that, for maximum flexibility in fine tuning.
Having said all that, quickdtoo's method sounds even better!