But I infer from the replies this is unlikely. Is that because to move the stylus off center at all it would actually require a movement of the whole head shell, like when one is adjusting tracking?
It's because any forces the stylus / cantilever / suspension assembly is subjected to during proper cleaning are equal to or LESS than the forces it will be subjected to during normal playback. You ever cue the needle onto the lead-in of a 45 RPM 12" and watch it SLAM into the 1st music groove? Or accidentally drop it a bit onto the vinyl without aid of the cueing lever? I've even had an end groove fail and watched / heard my expensive stylus eat paper label a couple times. It should be fine.
On the other hand a cleaning lady with a feather duster can exert snagging forces 100X - 1,000X greater than the above forces. That'll kill your cartridge dead, every time! These things are robust within "expected forces" of a certain range. Keep within that range, and try to relax!

