No reason it would not work. It's the same principle as a counter flow, sort of. The hot wort flows through tubing being cooled by water. You can regulate the flow by restricting it after the pump to slow it down so there is longer contact with the chiller.
Another idea along the same lines is to get or make a second immersion chiller and run the tap water through it in an ice bath before it goes though the one in the kettle.
I have the same problem in the winter when we are in Florida. The ground water temp is around 75°F but only do 5 gallons there so the old kettle in the sink ice water bath works.