I back the drag off on all of my reels... even between outings. I know for 100% sure that it certainly it can't hurt 'em!
I also used to take the lines off of the reels I didn't use during the winter. The newer lines coupled with large arbor reels just don't seem to need that. Besides, the spools lines come on aren't that much larger than those on large arbor reels.
Now that you brought this up though... darn it!, I will take the lines off of my smaller conventional reels this winter. Especially the lines from reels that don't allow for much backing.