Brian - the only real way to know is to put a DC VOLTMETER on your battery terminals.
Without shorepower appllied the battery should read 12.6VDC or so if charged.
When you conenct to shore power the on-board converter/charger should operate and charge your battery. You should see the DC VOLTAGE jump up to 13.6VDC when connected to Shore Power.
Once you see 13.6VDC on the battery terminals then operate the battery disconnect switch and see if the 13.6VDC stays or falls back to the 12.6VDC reading on the battery terminal.
Another way to do this is watch your ceiling lights in the trailer that are 12VDC lights. This may not work for you if you are using REGULATED TYPE LED BOARDS.
You should be able to turn the ceiling lights 'ON' when connected to the battery and not on shore power. If you connect to shore power then the ceiling lights should get a little brighter telling you the on-board converter/charger is hitting your battery terminals.
Using the digital VOM is the better way to do this as you can read the actual DC VOLTAGE. These meters are ranging from $7-$20 (WALMART-LOWES-AMAZON-any number of Auto Parts stores). Harbor freight gives you one FREE with purchases over $25 I have heard.
I carry one of these very handy meters in my RV TOOL BOX. takes all of the guessing out of the picture...

Roy Ken