Case runs a driveshaft off a damper.. Here is a breakdown. I dont remember it having any lube line but you should check, mine is 1,000 miles away. If there are no hydraulic pipes from that damper to the trans i cant see it mixing. The driveline is all gear, left and right trans.
What is making you suspect this? the trans may have a motor oil grade lubricant. Lotta the older stuff just ran 30WT in everything.