It depends on the type of seals Squish .If they are double lipped ,in other words sealing lube in and dust out you only apply pressure until you feel resistance .Any more will blow out the seals .A grease gun has like 5 to 10,000 psi .
On a single lip which is just dust exclusion only you could pump the whole tube in .It just squeezes out the seal .That type seal kind of acts like a one way check valve ,sort of .
Now I have no idea what type seals a praticular chipper bearings use ,that example is just generalities .