you can do it, but if it gets unplugged the solar charger will continue to draw power from the battery, so its not a great solution for unattended maintenance..
If you had fixed panels and used a couple diodes to isolate em its workable.. if shore power is lost the fixed solar can keep things going.
This is not really a huge issue as the quiescent draw on decent charge controllers is low, typically 10 - 20mA, so it would take a looooong time to hit the LVD on a 105Ah battery. However, there is also no reason not to leave the solar panels in the system. As long as the panel voltage and the power supply voltage are close, you don't even need diodes.