If your dealer did not do it; you should definitely shock the entire water system with bleach to try and sanitize it.
This is even done to brand new houses before first use.
This should include ALL the water piping including the hot water heater, ice maker and supplies to all faucets and showers.
Sealed up water systems will grow stuff when they are not flowing. Your water tank is vented to the air and it will DEFINITELY grow things when left stagnant. I don't know how much time it takes, but I would not drink water left stagnant in the tank for more than a month and then only if filled with chlorinated water.
I can't leave water from my well in the tank for even a week without getting things growing. I have to drain it and let it dry and then shock it with bleach before using for any drinking purposes.
If you only use the tank for flushing you MIGHT be OK.