The batteries should be used at all times when connected to shore power. They provide and additional voltage stabilization and noise filter for all of your DC electronics.
I'm with sch911. In fact, I always turn the battery disconnect to ON every time I plug into power. When I disconnect I unplug the power first then turn off the battery disconnect switch.
At home, after full charge, I disconnect the power to avoid overcharge and then turn the battery switch to off.
This is the practice which was recommended to me and which I have followed with four fifth-wheels for over 18 years.