If you run a check valve from muffler to the fuel tank you will then need a pressure regulator. I would imagine it to be a rare set of circumstances when you did not need the pressure regulator.

Many years ago, when I was flying pattern, OS decided to cheat in the horsepower race by hugely increasing the size of their carburetors. They began using the carb for the 1.08 on their then new .61 FSR. The carb was so large that they fitted it with a throat restrictor. The problem was, even with the throat restrictor, there just wasn't enough air flow through the carb for it to work right. Yeah, it was okay as it was for sport flying, but not for pattern. A pump/regulator was needed.

Rossi, on the other hand, had engines that developed their power through porting/engineering. They ran smaller flow carbs, but still produced more horsepower because of the sophistication of the innards of the engine. Those Rossis did not need a pump, for the most part.

Ever since OS fitted their .61 FSR with too large a carb for good throttling, we have had this problem of having to run a pump/regulator. Before that, most engines ran just fine with muffler pressure only. I wish the manufacturers would begin reducing the throat size of their carbs and begin utilizing better porting/timing for further horsepower increases. In fact, most engines are producing more horsepower than we really need these days. They can further reduce carb throat sizes to accommodate 3D throttling requirements. Enough of this blasted horsepower race. Tractability (engine throttling) is at least as important as gross brake horsepower on a dyno.