My big concern would be that the ice bath would not cool enough and would melt before much of the wort makes it through. I tried having my cold tap water run through a small immersion chiller in an ice bath before it went to the big immersion chiller in the pot. The ice bath melted into lukewarm tap water in under 2 minutes.
If I were you, before I ever got it near wort, I would test it by running hot tap through your chiller in an ice bath and see how much of your fermenter you fill up before it all melts (and see how cool it actually gets the water in the fermenter, too).