100% cotton sheets can get pretty pricey. i don't suppose it would be logical to insist on 100% cotton for the top then use a blend for the back. then again ... i've never thought it logical to insist on 100% cotton.
as redrummy pointed out, you will need to change needles more often - whether hand or machine quilting. but if it's a pretty sheet, and the cost of the sheet + the cost of a pack of needles is lower than the cost of using regular fabric for the back, i'd say go for it.