It kinda depends. If the pump is as original, then you can pump the grease zerk, on or off the car, and grease will fill the bearings and cavity...and then squirt out the hole on the bottom. If its already been filled, then any you add will force grease immediately out the hole.
That's if it is as original. The problem is many rebuilds do not have the stock style bearings. The stock bearings are open on the inside and sealed to the outside. When I was working with the 5 rebuilt pumps earlier this year, 4 of the 5 had double sealed bearings. Even if you pump all day on the zerk, no grease will enter a double sealed bearing...you are just filling the empty cavity between the bearings.
The down side...there is no way to tell a double sealed bearing without removing it from the pump.