I’ve thought about it, but not exactly sure why it should.
Admittedly, I am no expert in kart engines. That said, it doesn’t hurt a regular car. Doesn’t hurt any of the R/C 2 stroke engines I have used. Doesn’t hurt my 2 stroke blower or weed wackier. I can’t see how it would hurt. It will run lean for a short moment, but not long enough to cause harm.
The thing is, it will/should be running at idle for ~30 sec or so. I don’t see detonation really being a remote possibility.
It didn’t shorten the lifespan of my X30 and SSE 175 engines, both of which have made the regular time-before-overhaul with no trouble.