The large chainring on my mountain bike is missing a number of teeth on one side (apparently the side I like to go over rocks on). Is it harmful to the drivetrain to ride without these if I'm not having issues loosing the chain? At what point should i replace the chain ring?
While replacing any part comes down to when you want/can do it, you should replace any damaged part immediately. That's true whether you experience symptoms of failure or not.
Missing teeth on a chainring may not seem like a big deal until another one breaks off, causes chain slip or a dropped chain that sends you over the bars and into a tree or rock. Suddenly a missing tooth seems like a big deal.
As a side note, you should probably invest in a bashguard/ring if your knocking teeth off your chainrings!
Most non-pro riders will replace the entire drive train of chain, chain rings and cluster at once because of wear-in I would wait until you do that change over.
My cycle on this is usually 18 months or so. YMMV depending on the muckiness where you ride and how many km you ride.
On the other hand if you start getting chain-slip when using the ring then its probably time to do it.