Cuore_Sportivo_155

But not all the oil passes through the oil cooler, does it? If it's anything like the oil cooler on the 155 it's parrallel mounted, and a thermostat would open or close as needed.

It all depends if the cooled oil goes back to the sump, or continues it's way to the heads... If you have a VERY big cooler and the oil is redirected to the sump after it, you might just loose flow or pressure.
If it goes to the heads (as I would expect it to) your flow would not get affected.

Anyway, overheated oil is as bad as low flow... Engine parts will still overheat, and oil might burn in some areas.

Regards,
Cuore_Sportivo_155