overflow is before the P trap. Vent is after it. They look similar, and sort of do similar things, but they cannot be mixed.
I don't know if an RV can have an overflow draining to the outside. I do know that an RV tub can have NO overflow at all. Search on tub+"no overflow" in a search engine, and you'll find tubs made solely for the RV market.
So, overflow is connected before the P trap when it exists in the first place. An overflow is an open pipe so it would let insects come in to an RV when piped as you have described.