Could you use the Casimir effect to send messages across arbitrarily-large distances with carefully-tuned Casimir plates?

Obviously, relativity would preclude FTL information transfer, but as long as one did not try to measure any signal delay (i.e. impose an external reference frame of time), it would, in theory, be communicated instantaneously (presumably along an extra-dimensional Calibi-Yau surface/"brane").