If I have my math right..
The Shurflow 4008 pump is 3 gallons a minute. But lets assume its only half that going through the plumbing, or 1.5 gallons a minute. That will empty your 12 gallon water tank in eight minutes. Eight minutes is .1333 hours. .1333 hours times 7.5 amps is ONE Amp Hour.
So one tank of fresh water pumped through the system will discharge your battery
a little over two percent. That might be about 5% of the battery
power that one hour of the roof fan uses. If you have the smaller ten gallon tank, then its even less.
I don't think I would be highly concerned about the pump draining my battery. As for the noise, does it really run long enough to be an issue? My pump runs an average of two minutes total time a day. I can live with a loud pump for that long