Faster, as in higher frequency? Or faster falling/rising edges?
Higher frequency requires faster falling/rising edges because higher frequency means more transitions, which means more time spent transitioning, which means more losses (heating) from spending time in the lossy transition region. Without changing the frequency (and thus the number of transitions), the only thing you can do is to make each transition faster. Faster falling/rising edges means more noise.
If the driver cannot keep up, then the rising/falling edges can't be produced as quickly as you need them to be. Which means less interference, not more. However, there is such a thing as turning the MOSFET on too fast causing unecessary nois.- that's why gate resistors are used to control the rise/fall times for a driver that is oversized for the MOSFET. So even if you reduced the PWM frequency, you wouldn't reduce the primary source of noise since the noise is not coming from the PWM frequency as much as it is coming from the speed of the rising/falling edges.