If you don't have a voltmeter handy, you can do a quick check by turning on a (12V) incandescent light in the RV and then plugging into shore power while watching its brightness. It should get a little brighter when the converter comes on. Some LED lights would also, but not all—better ones have a regulator built in that keeps the voltage at the LEDs constant. (Simpler ones just use a current limiting resistor, and those would change brightness with changing voltage.)
If you have a really old converter, it's possible that the battery charge line is a separate one from the main output, in which case the test above could be misleading. You would also be well served to replace it with practically any newer converter; many of them had very very limited battery charging capability, only a few amps, and provided quite unclean 12V power to the rest of the RV. Chances are that you don't have to worry about that unless you have a vintage RV.
