Your water tank is like any fresh water holding tank. It's made of materials that are water safe, it's a closed system, and as long as your water at home is fresh, it'll last for months in your tank and be perfectly good. If you're on city water, or a tested well, don't worry about it sitting in the tank. For months at a time.
For lurkers that might stumble on this link, if your tank seems to suffer from smelly or funny tasting water, here's some guidelines:
1) Troubled water system: Add 0.13 X tank size = oz of bleach; run through each faucet a few seconds, let sit for a couple hours. Dump and refill.
2) Preventive maintenance: 1oz bleach / 60 gallons; pour it in, use normally.
3) Remove smells: 1&1/2 cup vinegar / 60 gallons; same as #2)
4) Sweeten water: 1/2 cup Baking soda / 60 gallons; same as #2).
Have fun on your trip and don't worry about the water. In 8 years of full timing, I have seldom run into water that needs any more then a treatment of #3) or #4). Even in Mexico.