If you've already got a hole with a pin, removing the pin shouldn't help. It can't flow enough water to matter either way -- it's just for air of course.
Now if you enlarge the hole, all bets are off. I realize you're not suggesting this.
Next time remove that heater hose on the housing. Fill through the radiator until fluid comes out the open hole on the housing then put the heater hoses back on.
Now continue to fill the system until full. Put the cap on and run it until its up to operating temp. Shut it off and walk away.
Check and top off after its cooled.
Thats the factory recommend way to burp that 4.0 or 2.5.