ChatGPT is super cool, but it does leave clues about the origins of the text it produces. If I were reviewing cover letters and saw one that was clearly AI generated, I would decline to move forward with that candidate.

Also, larger companies use expensive screening tools to chew through cover letters and resumes to highlight good candidates for a given position. It seems inevitable that the makers of said tools, many of which have some degree of AI trainability, will automatically flag documents that are suspected of being AI generated.

TLDR; almost definitely not worth the risk.