Just some stats, hopefully my math is correct, please inform me if its not (a very real possibility)
In 2013, the average annual electricity consumption for a U.S. residential utility customer was 10,908 kilowatthours -eia.gov
Ends up being roughly an average of 32 kilo-watt hours per-day
(Electric fish can generate a)
range from 10 to 600 Volts with a current of up to 1 Ampere, according to the surroundings - from OP's wiki link
600 volts and 1 ampere of current (600 watts) for a duration of two milliseconds. from Electric Eels wiki link
Watts = Amps x Volts and kiloWattHours = kiloWatts * hours
So one electric eel can generate up to (600 * 1 = 600) watts of energy / 2 milliseconds.
It takes 500 of these shocks to get to 600 watts / second, 30,000 shocks for 600 watts/minute, and 1,800,000 shocks to get to 600 watts/hour
32,000 watts/hour / 600 watts/hour = 53.3
1,800,000 * 53.3 = 95,940,000 shocks need to happen in each hour, for electric eels anyway. This is for one average American household.
That is 1,599,000 shocks per minute, or 26,650 shocks per second.
Since you also need to convert those shocks to some form of usable energy, (I'm not sure how that would be achieved), then there is also a loss of energy - so you'll need even more than that in practice.
Unfortunately, I haven't been able to find how often electric fish can achieve this level of shock, which is the next step I would need to do to actually figure out how many electric fish I would need, but that seems like a ton of shocks to me.
One other thing to note is that, in the electric eel's case, there are three organs which generate the electric shocks, which take up 4/5 of the eel's body. They can grow up to 2 meters long.
These organs are made of electrocytes, lined up so a current of ions can flow through them and stacked so each one adds to a potential difference. When the eel locates its prey, the brain sends a signal through the nervous system to the electrocytes. This opens the ion channels, allowing sodium to flow through, reversing the polarity momentarily. By causing a sudden difference in electric potential, it generates an electric current in a manner similar to a battery, in which stacked plates each produce an electric potential difference
This source seems to suggest that you would need 24 eels for 30 amps at 240 volts, and has a video of an eel powering christmas tree lights. Though most of the lights seem to be unlit for most of the time.
The heat pump uses 30 amps at 240v, the electrical eel produces approximately 1 amp at 500v. To make this happen, you will need an inverter to change the DC to AC, a voltage regulator to keep the voltage constant and 24 electric eels. Remember, the electricity produced is not constant, so this is really not a viable choice for power generation. Plus, you also need aquariums, feed and space for all these "free" power generators