Schematic for Parallax 6300.
http://12078.net/rv-stuff/Parallax_6300_Schematic.PDF
You are correct in that there is a relay that connects the battery to the unfiltered loads, that is mostly lights, when power is off.
When power is on the converter supplies about 5A to charge the battery and about 45A for other things.
The problem comes when the power is on. The voltage regulator uses an SCR (40A, 200V on schematic) in a form of pulse width modulation to charge the battery. For higher charge rates the SCR conducts for a long time, maybe many cycles. As the battery charges the SCR conducts less time as called for by the voltage comparator (SCR T106A1 on schematic). The T106A1 turns on when the battery voltage reaches the regulator set point and keeps the 40 A SCR from turning back on. The 40A SCR relies on the CURRENT in it going to about ZERO to turn off. This happens when the full wave rectified DC from the four diodes goes to zero at the zero crossing 120 times per second.
If you put a capacitor on the output of the diodes the voltage will NOT go to ZERO. If it does not go to zero the SCR will not shut off and the battery will try to charge to the sine wave peak value, around 18V!
This may not be exactly how it works but very close.
I know this will happen because I installed a fan with speed control one time in parallel with a light in the ceiling. The lights got really bright and measured 18V. I had to get out my scope to find out what was happening. I rewired the fan to the filtered output and all was well.