Always On adding a database outside of group I have a 2 node AG with a synchronous replica. I want to know whether I can safely add another database to the synchronous replica node, without adding it to the Availability Group.  

Does doing this carry any caveats?
That should not cause any issues at all. However, when connecting to a database outside of the AG, you will need to reference the server name instead of the AG Listener since the listener will always redirect you to the primary replica and your non-AG database will not always be on the primary replica.

Edit: Also keep in mind that actively using a secondary replica will warrant a need to license it.