If your water heater takes 1500 watts—at 12 VDC it will require 125 Amps to run it. If you have a 50 amp alternator, you'd still be shy of power needed by the inverter by about 75 amps. That means you'd draw down your batteries 75 amp-hours in the last hour of running the engine, just to heat the hot water. This is a significant portion of your battery bank capacity, since you only have two deep cycle batteries, and I'm guessing they're not 8Ds.
IMHO, you'd be far better off to turn on the inverter as soon as you start motoring, since, as the water heats up, the hot water heater will require less power, and more power will go to charging the batteries after a certain point. This would probably leave your batteries in a better, higher state of charge than doing what you initially planned, especially if you shut down the electrical side of the hot water heater for the last hour of motoring or so...
That said, I am quite surprised that the hot water heater isn't getting hot enough off the engine cooling system, via the heat exchanger coil inside the hot water heater. The engine should be running at at least 135-140˚ F at a minimum. If it isn't, then it is likely not running hot enough to be running efficiently. Domestic hot water temps are usually about 100-105˚ F, and the engine, even with conversion losses, should be able to get the contents of the hot water tank up that high. Since it can't, you probably should investigate why it can't. It could be as simple as scale build up in the heat exchanger coils in the hot water heater. Fixing this would make far more sense than killing your batteries, which is what running the electrical side will most likely do.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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