Can I damage a hall effect sensor with too much current?
I haven't chose a sensor yet, but it does need to be the type where it clamps around an existing wire.

Hall effect sensors work by detecting magnetic fields. I've never heard of a magnetic field sensor being damaged by too strong of a magnetic field. (Within reason - of course if it was extremely strong like an MRI then it might suck the sensor in and smash it to bits)
The only reason why the sensor might be damaged, that I know of, is if the wire is part of the sensor and you overload the wire so it burns. But since you're only looking at sensors where the wire isn't part of the sensor, that can't happen.