There is no reason that you can't use a sheet for backing and tie it. I've often used either cottton or flannel sheets and both produce good results. Sometimes I do a mixture of machine quilting (stitch in the ditch) and tying. It's your quilt, so experiement to get the result you like. I do find that if a quilt gets a lot of hard use that the ties eventually pull a little and shift during washing and may eventually tear out which is why I do some machine quilting to keep it a little more secure.