Without looking at your system I can't say for sure, but there area few things you can check for yourself to be sure.
Any good solar system should have diodes in the system to protect the solar cells from the power input from the "shore power" Actually the primary function of these diodes is to keep the solar cells from draining your batteries at night. Something a lot of people don't know is that solar cells will draw power if they are hooked to a battery and not producing power (when they are dark). Check your wiring diagram, it should show the diodes. I would be willing to bet you can find a former electronics technician to help you out with this. If your batteries are not draining fast at night you should be all set.
One drawback of the solar systems is that they usually not charge your batteries when you are hooked to power because if the solar voltage is lower than the voltage from your hook up you will only charge from the higher voltage source. This will depend on your solar controller. But if you really want to be safe you could install a switch to disconnect the solar system when you are on full hook up.
Some solar tips I have picked up over the years.
1. If you can spray water on the outside of your solar so that droplets form they will produce more power (the drops act like little lenses).
2. Panels that are too hot, or too cold will make less power.
3. If you can move your panels to track the sun do it 5 or 6 times in a day, less is inefficient, more is not worth the annoyance.
4. Your batteries will work the best when they are about 3 years old (hold the most usable power)
5. The first 10 charge cycles are the most important, try to fully cycle the batteries for these first 10 charges (fully charge them, and drain them to the same "low" voltage for these 10 cycles). Being good to your batteries for these cycles can add up to 2 years to there expected life. IMO It is worth the effort and annoyance.
So you know, my experience comes mostly from driving over the road electric cars, there are other long distance tricks we used to use, but they were used to squeak out extra miles at the price of battery life so I did not include them.
Good luck.
