Someone correct me if I'm wrong, but the Aux. pump is only to keep the coolant circulating when the car is shut off. Like if you're running the vent feature or just running the fan with the engine off.
Bypassing the aux. pump should then be of absolutely no problem at all to driving the car normally. Only reason the dead aux. pump is giving you a problem is because it's seized up and preventing any coolant to flow through. Bypass it though and that's no longer a problem. Only problem should then be lack of heat after a short while once the engine is turned off.
Cosmos Black/Black 1995 540iA M-Sport
BMW Individual Exclusive Edition, 1 of 65 total, 9/25/95 Build