Depending on washability, yes, if it were big enough. I would not make a quilt big enough for a bed that wasn't washable, because to me the utility of the quilt is as important as artistic merit, but that is my preference.

Art is meant to viewed straight on, at eye level. That's not possible when it's lying on a bed, so, no, I would not use a bed for display of an art quilt. It would greatly detract from the impact of the design.

That would depends on who lives in the house.
Just DH & me - yes
Pets? - no