As moey said, the heat pump would only run if the sensor told it to, this could be from normal heat loss from the tank and pipes.
Nyle sell 2 models, one that uses the electric element sensor that is maybe already in your water tank or a model which has a separate heat sensor that you mount at the bottom the tank, this is the model I have. The hp, maybe because it has the feed & return + sensor at the bottom, seems to heat the tank more thoroughly than the indirect coil and sensor mounted half way up the tank. In my case for our house of 5 adults it heats all our hot water in the warmer months.
Our basement before the heat pump, would be a bit musty, before I ran an a/c supply duct which has its own fan, we would run a dehumidifier but it made the basement warm and noisy. After I put in the a/c supply it still would smell damp and it could still get warm.
With the Nyle the furnace room is sometimes pretty cold, the door to the rest of the basement is closed but those rooms are now also cooler and no more damp smell in the basement.
To answer if the hp would work for you, if your tank is of a reasonable size - you should not get water temp swings, you could expect to save money rather using an oil burner, nobody can hear the hp running if they are in a different room in the basement or in the room above, it cured my damp basement, it cooled my basement, it could work for you, it certainly would reduce and hopefully elimate the time the dehumidifier runs if you use one at the moment.
Pump the water out collected by the hp rather than using a bucket. I use an a/c condensate pump, which goes via a little clear filter (to stop the bugs crawling in) to a couple of micro sprinklers in a garden bed. Hope to grow tomato's in there this year..
It is quite funny to watch it when the water gets pumped out..