Assuming you have painted (not stained) trim, then yes, the caulk is painted over when the trim is painted. If the trim is white (pretty standard), then the caulking doesn't always need to be painted where the trim meets the wall, if they do a good job rolling out the caulk. If they do a bad job, then you'll need to touch up the walls anyway. I would use a white caulk, not clear. Clear caulk needs to be painted over completely, everywhere. White caulk on white trim won't be noticed and is opaque, so it covers all dark lines where there are gaps.
So don't paint the trim before it's installed? Can't I paint it then install it? Thanks
Painting the trim first is much easier. If the caulk color doesn't match the paint color, then you'll have to touch up the trim paint after installing. I'd rather paint the trim off the wall and then touch up, than paint it all after installing.