Should all thru-wall home ac units drain out condensate in humid weather?

I'm new in humid central Florida and have two thru-wall room AC units. A large Freidrich one that also has resistance heating (for the couple of cool nights in "winter" here) and a small bedroom sized GoldStar one. The Friedrich does great and as I assumed all units did, drips condensate outside.

The smaller one was only being used at night with the bedroom door closed and the bigger unit off (to save elec. $s). Last week was the beginning of the most humid summer weather so I had the small one on one night (80 deg at 11pm, and 65% humidity, pre the weather report) with the door closed. I was cool overnight, but I also sweating... I began to wonder if a unit can blow cold air, but not be removing the moisture and instead be blowing it back into the room too?

I checked outside the next morning and some other time during the hot afternoon - and there was No dripping at all, while the other units was, as it always does. Looking up at the unit (on the second floor in the shade) I can see what looks like a black rubber plug on the face of the lower right corner of what I assume is the drain pan. I'd expected to see a tube - but not a plug...

Can a unit run right with no drainage?? I've even sensed a mild mildew-like smell when starting it up sometimes of a little while.

Any help will be appreciated!

Bill in St. Pete.

Not all through the wall unit will drain condensate. Some or most of the newer units have a pick up ring on the condenser fan motor which picks up the condensate and slings it on the condenser coil where it is evaporated and cools the condenser to improve efficenicy of the unit. This is dependent on manufacturer design.It is possible that the unit is not removing the moisture properly due to a problem with the unit such as a dirty air filter, dirty evaporator and or condenser. The comfortable indoor humidity range should be 40% to 60% @ 72 to 78 deg.F. To be sure the unit is operating properly and preforming at manufacturers performance rating it should be checked and serviced by a qualified HVAC technician Also, an undersized unit will not be able to remove the proper amount of moisture on a high humid/temperature day.