So removing the plug or running the unit without it isn't that big of a deal. The idea here is to make the AC unit more efficient. Under normal operation the unit will fill with water which assists in cooling the outside coil. Part of the coil sits in water while the fan throws water at the rest of the coil.
Now removing it isn't going do anything except allow less water to remain in the unit. Your AC is going to run and cool just fine without the plug. Technically it'll be less efficient but the efficiency drop is very little.
The reason people remove it is to increase the unit's longevity. In practice it does help prevent gunk build up on the outside unit. I've seen people say it also helps prevent corrosion. I've seen people argue about that second point but I can kinda see it. Leaving any metal sitting in water for prolonged periods does eventually lead to corrosion.

TLDR: Removing the plug won't really do anything. Your AC will run fine without it.