Kevman
I've moved the bottle to an underseat location with no problems. The tank serves as expansion tank for the heated coolant, also allowing the air in the system to escape as you probably know. The ideal location is where it is.
Sooo with that being said, the way the system works is... the coolant and air bubbles (that may be there) heat up, expand and the fluid (usually not much once the system has stabilized) gets sent to the tank. Because it is a closed system, upon cooling a vacuum is created in the system. The fluid is actually sucked back into the system.
It's important if you relocate to be sure that the hose running to the tank is perfectly sealed at the connection to the aluminum fill housing next to radiator cap. Make sure that the hose in the recovery tank is below the the fluid level there.
As an experiment if you have reservations about doing it. Use clear PVC hose and locate the resevoir on the ground next to the bike. Heat the bike up real good (not a problem with the VMAX : ) I even disconnected the fan. And you can watch it work.