In the meantime, Trevor Letowski is acting as the head coach, and he has the full confidence of the players. Moreover, he is in constant communication with St-Louis, and decisions are made collaboratively between the two coaches.
Recently, there was a surprising statement suggesting that Jim Montgomery, the current Bruins coach, could potentially succeed Martin with the Canadiens. This raised questions, but once again, there's no need to worry about St-Louis.
In short, no, Martin St-Louis will not leave the Canadiens, not for a good while. The only reason the opposite would happen is if he leaves the organization on his own terms.