Oh yes! In fact, I have a rocking chair that has a slot near the top of the back that's just perfect to slip a folded quilt through. When a quilt is entirely finished, but before it goes to its new home, it lives there for a while. Then it just feels like it's supposed to be there!
I made a bright blue and yellow ducky baby quilt a while back and have had many occasions to send it on to a new mama, but .... it has stayed with me instead. (Now if my daughter gets on the ball and gives her 3-year-old a baby brother/sister any time soon then I may can part with it!)