Some Graph Tech customers have tried this with a simple Y-connection and found that the two electronic circuits interfere with each other if they're both powered on. If either is shut off, the other one works fine, so yes, you can run one or the other, but not both at the same time.

The difficulty with running two systems from two manufacturers off the same set of pickup saddles is that there may be loading, impedance mismatch, or other unpredictable interactions between the two electronic systems, when they share a common node at the connection to the pickup. There may be another way to do this, perhaps with some kind of buffer between the pickups and the circuits, but the solution remains undiscovered at this time.