No. It is three fouls by the same player without that player making an intervening legal shot.Perhaps I used the wrong term for pool. In snooker the fouling the player can be sent back in, and there is no limit if he keeps fouling.
So it is not "3 consecutive fouls" but 3 fouls in the same game/rack?
You scratch on the break.
I run two balls and then send the 3 ball up table and freeze the cue ball to the back of the 9 ball.
You fail to hit the 3 ball. I inform you that you are on two fouls (this warning is not required by the rules)
I play the 3-4-5 and play safe on the 6 ball.
As you come to the table, I warn you as required that you are on two fouls. You manage to hit the 6 ball but the cue ball scratches.
I win because you fouled three times without making an intervening legal shot.