Sounds like a plan to me.
I normally just buy a couple of bags of ice. I add the ice to a cooler with some water and then use a sump pump to send it through the chiller. I dont use the ice water until I am below ~90F though. Its a waste of ice. Even if you dont wait until below 90 to use your cooled water I would still wait until you are below 120. Your heat transfer rates are still really high at that point. When you get below 100F is when the cooling rate starts to significantly slow.
To get down to 90 I use my immersion chiller and set the boil kettle in a big tub of water. I empty out the tub twice before I get down to 90. For ales I'm pitching within 15 minutes and Lagers about 25 minutes.
"I HATE beer" - My wife.