Yes you can use your inverter for short periods provided it has a transffer switch of its own.. Now I can bypass a auto transfer switch.. but alas I do nto feel comfortable telling others how.
If the transfer switch is a 3-way (Short/Genny/Inverter) and no inverter sub panel I would avoid all 120 volt use.
In my case the line is like this (simplifed stuff left out)
Shore---ATS--_main breaker box--Branch (30 amp)--Inverter---Sub panel--Stuff
If yours is like that you can still run the "Stuff". But not for long cause it eats batteries.
Oh. I do have a way to plug in my converter independent of the RV that extends the "Stuff" run time to.. Forever