If for the sake of argument we are plugging this into an SNES emulator running at 60Hz, then the stack between the USB gamepad and the emulator already has to handle that the gamepad is not rigidly synced to the emulated SNES and will presumably take every input from the gamepad and use it as the emulated input to the SNES next time it asks, unless a new one comes in first.

At slightly faster than 60Hz, the net effect will be that the delay between input and having an effect on the SNES will wander about 1/60th of a second over time, as the sync varies, and every once in a while a particular input will be overwritten before it makes it into the emulator. It may be very difficult to perceive this, though, due to other delays already built into such a set up. On a real SNES, it would be right on the edge of perception anyhow.

Being very close to the poll rate but not quite there is probably near the theoretically worst case. It would probably be much better to poll at 240+Hz, cutting the latency between input to a consistent 1/4ish of a frame. However, I doubt this improvement could be "felt" by very many people at all.