First, vinegar does kill salmonella, E coli and some other bacteria but overall it is not a great disinfectant and certainly no where near as effective as chlorine bleach. Why not just use bleach since it is much more effective.
Hot water tanks can develop quite a bit of scale. Pumping some vinegar into the tank and letting it soak should help, but I would certainly not pump that residue into my fresh water tank or even through the hot water pipes and faucets. Pull the plug and let it drain out of the tank instead.
I have never had an issue removing the bleach from the water system. I drain the tank, add a partial tank of fresh water, drain again, and then fill up.
There are plenty of campers who do not sanitize their fresh water tanks. Most of them do not drink water from the tank. Even so I recommend reconsidering. Sanitizing helps to remove the pink slime (pseudomonas bacteria) that grows in water tanks. It is relatively harmless for most people but can start to clog faucets. I am also concerned about Legionela. I had a friend who was very sick from Legionnaires and that bacteria is often found in RV hot water systems and the shower head. It takes little cost, time or effort to sanitize so I cannot understand why anyone would skip this.
