Is it possible that Cloudflare blocks the Wordpres admin-ajax file alone or with default configuration?
No, I have ran countless Wordpress sites behind CF in the pasty and have never had a problem with admin APIs being blocked. The only issue being that you might need to disable the WAF for
/wp-admin*, however this only applied when on the Pro/Business plan.
I second @judge’s assessment.
What problem are you seeing?
If Cloudflare is blocking something, it would usually show up in the Firewall Events Log.