Your incoming cold water there is likely to be near freezing. So the heater must raise the water temperature something in excess of 70-degrees. Since the water is only in contact with the heat exchanger for barely a second or so, it much transfer a LOT of energy in a short time. As a result, you'd need a really significant power input. It is likely that you would need to update your electrical service, but it could work...it will be expensive because of the power upgrades you'll likely need (and this may change your monthly base cost since you'd have a bigger possible use...depends on how your utility bills things). You'd need to have some some special valves installed so you could blow the heater dry, as it would likely be damaged by even a small amount left in the heater.
It would be far cheaper to dump the existing tank when you want to leave. Energy-wise, you aren't really thowing much away to do it a few times a season.