Balaton,
On the 747-200, The #4 ADP (air driven pump), or #4 ACP (electrical pump) is used to pressurize the parking brake before start, and to provide braking during tow in the event of a tug failure.
The #1 ADP or ACP is used during pushback and tow to provide power to the body gear steering.
I don't know about the 767, but in the Classic 747 we can't transfer fluid. A veyr small amount can be transferred through the brake system, but it's inconsequential, and not the reason that the #4 hydraulic system is powered up prior to engine start.