It depends why you want to run your generator I guess... If it is to re-charge the batteries then you will have to leave the battery connected to the system.
It also depends on where the battery disconnect switch is installed. Alot of battery installs have a few things direct connected to the battery terminals which may be on the battery side of the disconnect switch and not coming off the 12VDC distribution panel.
Leaving the battery connected to the trailer without some sort of trickle charge will end up with a discharged battery is a quick as a few days running all of the parastic loads in the trailers thus the reason for the disconnect switch in the first place.
If you are parked outside at the storage place a good low level solar panel is great for trickle charging the batteries all day long especially in Arizona...
Some people don't like leaving the batteries installed for fear of thief... Don't think for a minute being at a storage facility makes it all safe from thief... Alley cats will jump the fence... My luck would be there is a not responsible for thief clause in the contract haha...
Just my thoughts
Roy Ken