Yes, you can check for charge.
Using a volt meter. I would start by unplugging the rig from shore power. Test for voltage level on the battery(ies). Now plug in the rig, and check to see what voltage level is.
If it is unchanged, it is likely the battery is not being charged.
Go to 12 volt DC distribution panel. Look for a main battery fuse. Check for voltage there.
Good voltage there look for circuit breaker or fuse near battery.
No or battery voltage, locate the converter. Note for make and model! Look for reverse polarity fuses. Depending on make and model of converter determines if it has any.
Check for 120 volt AC power to converter.