Welcome to the forum! No, your Navion will not charge the engine battery when plugged into shore power. It is actually designed this way so don't waste your time looking for fuses, relays, or wiring issues.
You have two options to reduce battery drain: 1) Remove the engine battery ground plug (it's just above the accelerator pedal) or, 2) Install a Trik-L-Charge. The Trik-L-Charge is preferred if you have solar or you keep your motorhome plugged in when you are not using it.
The Trik-L-Charge borrows some current from your house batteries to keep the engine battery charged. In installs on the charge relay under the passenger seat and takes 20-30 minutes to install. Do a search for install help if you choose to go this way.
Roger & Mary
2017 Winnebago Navion 24V
2014 Tiffin Phaeton 36GH (Sold)