[DerkPerk]

You are exactly right in your diagnosis. Should have been T'd into the tail piece of the sink drain.
I'm not one for removing the overflow plug unless it is piped to a obviously seen place.
Also a trap should be installed according to the manufacture design, most likely yes. You could get away from one ONLY if the condensate pan is on the positive pressure side of the blower but guessing that isn't the case because of the smell.
You could eliminate the smell by adding a trap next to the unit but it would have to stay primed or the smell will return. I also recommend changing the drain tie in.
Typical residential hack installer. Good luck.