It's unlikely that firms will use automated AI detection tools, because they don't work.
IME using AI it creates horrid prose with certain patterns like
- lots of unnecessary adverbs like "genuinely multispecialist"
- "matches how I work best"
- "intersection of X and Y"
- "combines X with Y"
I am sure if you are in recruitment and you come across these kind of patterns you just click "reject", without going to check an AI detector (which doesn't work).
OTOH if you use AI and edit out the repetitive AI quirks, they are not going to notice.