That's one of those "it depends" issues. For any RAID level other than one, I would say "Yes, you will." But many people on these forums have succeeded in booting from an orphaned RAID1 disk. I haven't seen anything about moving an intact pair.
So. "It depends." It will probably work. Don't count on it. If you have a good backup when you change motherboards, it won't matter anyway.
Even if I can't move the pair, I ought to be able to move over one drive and rebuild the second one right?