Doubt it will help with the wobble of the distributor shaft. A little grease is pushed in as it works its way out from around the shaft. That's what the spring loaded plunger is supposed to do.
If you have wobble in the distributor shaft you need to either rebuild it or get another distributor. The bushings inside the housing that support the shaft is worn, and perhaps the shaft is too.
Nothing is inside pushing against the shaft. Only grease is pushed through the hole to lube the shaft.
