Does blocking AI crawlers hurt my Google ranking?

It depends entirely on which token you block, and the two cases are not close:

• Google-Extended is free - Google says it “does not impact a site’s inclusion in Google Search nor is it used as a ranking signal in Google Search” (Google Search Central).
• Blocking Googlebot is not - AI Overviews and AI Mode are part of Search, and Google states that “robots.txt directives for Googlebot is the control for site owners” (Google Search Central).
• So there is no half measure on Google - you cannot stay in Search and stay out of AI Overviews.
• Other vendors’ tokens do not touch Google - GPTBot, ClaudeBot and PerplexityBot rules are read by their own crawlers only.

Blocking Google-Extended costs nothing in Search. Blocking Googlebot costs everything.