I can run everything in my trailer with my battery disconnected...cables off...because the job of the converter is to take 110V and turn into 12V for the 12V system. No battery should be needed.
If your slide wont go out my guess is you had a mechanical problem. Or your inverter is not working as it should.
It really depends on how the trailer is wired. On mine I can not operate the electric slide with the battery disconnect on, but I can operate the hydraulic slides. I can also operate the landing gear with the disconnected engaged.
The lingering question is if it works now.