When you use the proper long adapter cord to plug your shore power cable into the standard 120VAC 15A/20A house receptacle the 120vac will feed the trailer 120VAC Power Distribution Panel the same as the shore power cable source did. The only difference is you only have the 15A or 20A Service available to use.
You have to go and trip the AC breaker for any of the high wattage items and maybe only have your 120VAC receptacles turned on and most important to have the breaker for the converter/charger ON. This is what charges your battery as well as providing 12VDC to the 12VDC Power Distribution.
You can have the same question for plugging your shore power cable into your generator set. It provides 120VAC to everything but you will be limited to the wattage of the generator...
My generator is a 2KW and my converter/charger will want to draw 1KW when it is charging my batteries. So I only have around 600watts left over to run a few of my low wattage appliance...
All clear as mud huh... I am plugged into my 20A Service receptacle in my garage here all the time when my trailer is at home...
Roy Ken