Cute idea, but I don't have time (or great ability, lol) to sew. What if you offered for them to send in however many t-shirts and you do the sewing?
Also, I don't know that I would market it as a baby quilt. How about just a mini-quilt (for anyone) out of anybody's t-shirts? I have a stack of old t-shirts that I've held on to, but I wouldn't necessarily do a search for a daddy quilt, kwim?