Shouldn't be a problem. We run multiple systems behind a few load balancer setups and doing certificate authentication; never had any issues with it.
If you're getting a "bad gateway" is that ONLY with the certificate auth? Does it happen when accessing any other pages or like HTML forms schemes?
One thing to keep in mind with cert auth, is that whatever load balancer you're using should not be doing SSL termination, that will completely dork up the cert auth. Needs to just pass through the request to appropriate active server.