There are a ton of variables here - especially the type, size, & age of the battery. Sounds like you are planning to keep the draw on the battery to a minimum.
Just a wild guess here - I would say 2-3 days for sure, after that - ?
One thing you could try is unplugging the camper at home and letting it go a few days to simulate dry camping and monitor the voltage with a meter. The camper will probably function on a charge as low as 11.8 volts, or maybe less, but running it that low may permanently reduce its performance. You can search on here for more threads that detail % of charge vs voltage.
If you want to camp longer w/o electric, a second battery is an easy upgrade.
2005 F-150 FX4
2013 Rockwood Roo 23 IKSS