I think you'd definitely need a quadrature setup to tell the computer(?) when the tape was being pulled out of the housing or allowed to reel back in. Also, if the tape was wound around the shaft of the encoder, there would need to be some compensation, because the encoder would turn fewer revolutions when there are more wraps. Think of it this way: put a one-inch diameter wheel on the encoder shaft to simulate wraps of tape. For every revolution of the shaft, 3.14159 inches of tape would be pulled out. Put a 1.25 inch diameter wheel on the same encoder, simulating more tape wrapped aroung the shaft. At that point, for every revolution of the shaft, 3.92699 inches of tape would be pulled out. I think that'll be tricky to compensate for.
JB