with the brakes,
if you set the park brake with system B, then secure sys B,
turn on sys A, and release the park brake, there will be a small transfer of hydraulic fluid, or vice versa!
The same effect will be had with the reversers, since they can be operated open with a 'normal' hydraulic system, depending on the side, and closed with the standby system.
But these are things one would do intentionally, not something done unintentionally!
In response to your Q, I don't know of any otherway to transfer fluid from one hyd sys to another, on the 737NG.
Think of your current procedure when being pushed/towed without the steering disconnect pin in place, don't you toggle the system A pumps off and on, without changing the on status of system B!