That's very clever but feels like breaking the game slightly.
In the game Bridge, which involves communication between competing pairs of players, you can communicate a suit and a number, but it is meant to have some kind of meaning within the game, so I think strategies like this would be illegal.
There's no requirement for the bidding to be natural, there are plenty of artificial bidding systems -- the only constraints are that the bidding system you are using must be known to your opponent (to enforce this, I believe that on a bid your opponent can ask your partner what this bid is supposed to communicate), and that you do eventually have to play your bid so it can't match your cards too badly.
In the game Bridge, which involves communication between competing pairs of players, you can communicate a suit and a number, but it is meant to have some kind of meaning within the game, so I think strategies like this would be illegal.