Linkway,
you do not need cold water as such. If you are running from the faucet, the room temp water is very adaquate.
You do not need to pre-chill if your supply is from the tap.
An "Ice Bucket" is used when re-circulating water with a pump. The ice is merely a way to prevent the reserve water from getting to hot.
However, if your condenser is so undersized that it can not keep up with the demand of needed knock down power,,,,,,then your system is prolly very helpful.
Can't you recover the waste water and water the garden,,,,flush the toilet,,,,,wash the dishes?
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