I’m gonna piggyback off of TJ a little bit, and say that you can overlap your throttle and braking slightly. In most karts (anything not direct drive) a centrifugal clutch is used. This means it takes a short moment between getting on the throttle and the kart starting to accelerate. This time is acceptable to be overlapping the brake and throttle, but you should not be trying to keep the revs up on a kart while braking. If that’s a problem, you are getting on the gas too late and should likely need to adjust your line a bit. I used to do this all the time at my home track at a couple turns, and still find myself doing it occasionally.
Like the other guys were saying though, using gas an brake at the same time is hard on both the clutch and brakes. From a driving standpoint, using the gas and the brake is trying to do two inverse things at once, accelerating and decelerating. This will, as stated before, increase wear and is not the quick way to get around a circuit.
Don’t worry too much though, you’re not the first and you won’t be the last to do this. I blew a hole in two pistons before we realized I was riding the gas through turns. That keeps the engine temps really high and, in our Yamaha at least, eventually burns through the engine.