This isn't going to work, you're going to have all kinds if issues trying to maintain the proper level inside the PTU.
A few issues. The PTU is a vented case, not filled to capacity as there is a void in there. It is also not designed to see any sort of pressure or you'll push oil passed the seals.
In the system you are thinking of, as the oil passes through the cooler, it will become less viscous, not much, but enough to create a "backup" and it will spill out the vent.
If the system was a closed, non-vented system with the ability to take pressures, or in a system that has way more capacity and "reserve" empty space, this could work, but I foresee a ton of oil spewing from the vent....