I switched my server over to PHP-FPM instead of SUPHP. I cannot tell for sure if my cron jobs are working. Is there an easy way to tell this?

Check the "Last run" value of tasks in the Tasks list - if it's recent, then it's running. If not, then it may not be.

Other options: maybe edit the cron job so that it sends an email upon completion/failure?

It looks like tasks are running correctly. And it is funny you mention having the cron job email me to verify this, because that is what alerted me to a possible issue. I have 3 cron jobs set up to optimize databases that normally email me after completion, and now they don't. This all started after switching my site's php handler from SUPHP to PHP-FPM. I suspect that I could have resource issues, perhaps memory or other settings that I need to tweak.

You can always run the command manually at command line and verify it runs successfully. If it does, cron should be able to run it fine too.