A hole of this type, although usually of a smaller diameter, is used by some other manufacturers like Dana Corp to allow for pressure relief in cold weather on some of their driveshafts. In the Dana lubrication manual linked earlier in this thread they recommend covering the hole with a finger tip while lubricating the drive-shaft.
I bet the previous owner drilled that hole after reading a bunch of "scare" threads in the 80s section about how excess lube was going to blow his transmission into the rear of the engine damaging both.
No such thing as too much grease in this system. It's designed to be filled with grease until it purges past the seal. I would look elsewhere for the cause of the vibration.