A gomoku variant... I'm asking if it would make sense

It is the usual rules of gomoku, but without swap rules. White is compensated for the first move by having an additional turn at the end, when black has completed a row of 5 stones. If white can complete a row of 5 stones with a single move, then it's white win instead of black win.

Would this work? Any idea?

Hmm indeed someone pointed out that white simply wins by copying black moves... oops...

In my opinion, Connect6 sorted out that problem (black advantage)...