I would think that so long as the remote turn on lead of your amplifier is not receiving any voltage and the amplifier is off, it would not have any draw whatsoever. You could verify this by doing a parasitic draw test real quick when you install your amplifier to the battery. I'm certain there will be no draw. There's no reason for there to be as the amplifier doesn't have any memory settings that would require it to draw any constant power to retain them. I have pretty much the same set up you described as far as a single engine, dual battery, and on board charger and this is how I have my amplifier wired (to the non cranking battery). If by chance there is a draw, you charger should be able to keep up. Without knowing what type of Pro Mariner charger you have, if it has any type of smart charger technology- it will automatically come back on and charge your batteries whenever needed.
J