Is a house battery necessary if plugging in at campground?

Besides the obvious required use for the brake.

All you lights run off DC which is off the battery. Most RV fridges AND air conditioning units need the 12 volt for their thermostats. These 2 will come on but when they reach the required temp and shut down they will NOT come back on without DC power to them.

So yes you need a battery. I found Walmart had the best price for them. They are less expensive then a car battery so don't sweat it.