I thought I'd seen someone mentioning a similar idea a short while ago, but can't find the post. Rather than a counterflow chiller they were talking about an immersion chiller as both the herms coil and chiller. If I'm picturing your idea correctly, I'm seeing the wort going through the same way both times (mash and chill), while during the mash you'd have warm water being pumped through the chill ports, and cold water during the chilling. (Or are you talking about putting the whole chiller into the HLT and running the mash through the chill water ports?)
Assuming the first method I mentioned, what I'd be worried about is being able to maintain a mash temp using a counterflow chiller. While it should be able to maintain temps fairly well once you hit a point, you'd have to test out the best spot for measuring your temps so that you didn't go past your mash temp.
As far as getting it clean, I don't see it being that big of a deal since the wort is going through the same route. Pump some boiling water through before the boil is finished and it should sterlize/wash it pretty well. Unless you generally get chunks of grain through during the mash recirculation, you could probably even skip a rinse, although you'd have all the time of the boil and it might give you some piece of mind.