Yes! We do it all the time. When we demonstrate RC4 products at tradeshows, we often have a battery charger connected at the same time. We need to run all day for several days in a row, so it’s very important we keep our batteries charged as much as possible.
When a charger is attached, the voltage at the battery terminals will be higher than normal, but it won’t get high enough to cause any harm to your RC4 receiver-dimmers. If all your dimmer levels are at zero while doing this, that’s the end of the story.
On the other hand, you might want to operate the dimmers while you have the charger connected (just like we do in tradeshows). In this case, keep in mind that when you bring a channel up to full you are delivering more than 12V to your load. This will reduce the life expectancy of 12V lamps, while also making them appear brighter than usual. If you are driving LEDs through a current-limiting resistor, higher voltage results in higher current, and you could be pushing your LEDs beyond their rating. I would run the channels at less than 100%, just to be safe, when chargers are connected.
Jim