So it looks like they do check credit when adding joint holders, and I guess that's what the soft pull is for. The form I received said that they will "evaluate" my information and if I'm approved I will be added as a joint holder. There is also a clause saying that they reserve to right to check your credit report.
I've decided to just remain as an AU and see how that affects my score for now.
Sounds like everything in this thread has been cleared up but yes, Chase reports AUs, and yes, you can add a JOINT user to an establish account using a special form.