What you're proposing might help, but it's very far from an ideal solution and I wouldn't recommend it. A block heater (at least one made with appropriate materials) won't cause water purity or safety problems. Since they're made for use in engine blocks, though, block heaters generally wouldn't be made with food-grade materials, and certainly wouldn't be certified for use on potable water systems. That isn't saying they would contaminate the water, just that they aren't guaranteed by the maker as not doing so.
There are bigger issues in terms of efficiency and effectiveness. The fresh water tank is usually not insulated, so there would be a good bit of heat loss from it (and heat gain in the interior of your RV if it's within the envelope of the living area). It also holds a comparatively large amount of water, so it would take a long time and a lot of energy to warm up the tank appreciably. Any cold water that you used as such also represents wasted energy consumption in needlessly heating the water.
I suspect at least some block heaters, and probably all, have a thermostat to shut them down at some temperature. It's entirely possible that this may be lower than normal room temperature since they're generally employed during very cold winter months only.
With proper plumbing (basically a valve in a new pipe connecting the hot water line to the tank fill line), you could use your existing water heater and water pump to heat up the water in the fresh water tank. It still wouldn't work very well and would waste a lot of energy, of course, but the cost and complexity and any safety concerns in hooking things up would be largely avoided.
I suspect, however, that the most satisfactory solution would be the obvious one—replacing the water heater with a more capable unit, probably a propane-fueled one given the electrical supply limitations of RVs.
