Is it OK to use a system cron to trigger a function hooked into the AJAX API

You are using the system cron to trigger a function hooked into the AJAX API, not, as your title reads, using “admin-ajax.php to run a real cron job”. You are doing exactly the opposite of what you wrote in the title (I’d advise editing that).

Yes, that is perfectly fine. I have advised using the same technique in fact. All you are doing is making a request to the server on an accurately timed schedule, instead of waiting for a random request from the web. It is no different from any other request to the server.

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