 It is not difficult to see why this must be so. If Alice and Bob share a pair of systems that are entangled, then the probabilities for the results of any measurements Bob might make do not depend on whether or not Alice also makes any measurements (this is the quantum mechanical no-signalling theorem). In exactly the same way, the pattern of detections at the screen cannot distinguish mere entanglement with some other systems from the actual use of those systems for detection at the slits.