Yes, there should be at least 1/3 cup of oil in the u-joint "housing". The u-joint housing gets it gear oil from the transmission. That is one good reason for regularly checking the transmission gear oil level regularly.
You can loosen the u-joint bell/ball cover at the transmission and by unscrewing and sliding back the rear cap/seal. Slide back the ball/bell (be careful not to break/rip any of the paper gaskets) and inspect the u-joint. It should slide up and down in the trunnion bushings/bearings. There should be little/no lateral looseness.
