You basic concept is correct, it can be done and would work. There is the chance of freezing your water tank though as you do not show a circulating pump.

However, are you increasing your energy usage by having the water tank and pump circuit?

If you wrapped the copper tubing around your vapour condenser directly and made that the evaporator then you would save costs and improve performance. There may be a need to improve the control of the fridge circuit but I'm sure that there is a get-around somewhere.