Can you add a backing to a store bought blanket?

OK I'm not sure if this is even the right board to ask on if this is do able or if I'm setting myself up for a let down...

Our daughter received a throw sized quilt with minky backing for her baby shower. Now its the only blanket she will use to sleep (I think its the minky material she likes so much) I bought a little comforter, because the quilt doesn't seem like enough for winter, but she doesn't want to use the new comforter. Would it be possible to add a minky backing to a store bought comforter and either bind the edge or just try to fold over the fabric and sew it as close to the edge as possible.