river supply question

[Dog Soldier]

If you are referring to engineers being able to ferry infantry across the river in little assault boats, then the answer is....
Yes, you will have supply as long as your infantry on the far bank stays next to the engineer who ferried them across. This movement was not for conducting advances, but to form a bridgehead on the far bank to cover the bridge engineers while constricting the bridge.

If you do not have any bridge building engineers, then you will need to link up with another established bridgehead (in the center of the map for the scenario you mention) or go without supply.

Good luck.

Dog Soldier