Are table joins not allowed on branched versioned data? I keep getting a user permission error on both the version I created and the DEFAULT, and I'm the data owner. I think my best option at this point is to download the layer, perform the join, and then publish and version it again. Versioning seems like it has it's limitations, and really just for basic editing work.
Once you branch version data (and publish as a service) you cannot connect directly to the feature classes in the Enterprise Geodatabase. So I do not think the join would work there, you may be able to join to the feature service.
What is it you're trying to do, exactly? If you write your SQL carefully, it's possible to use a Query Layer against branch versioned data.