Counterflow chiller, no cold break?

I used some newly acquired equipment for the first time last night -- a keggle with a manifold, and a CFC. I used to use a submersible chiller, so the wort was chilled before being transferred to the carboy and the gyle was left behind in the kettle. With the CFC, since the wort is cooled as it transfers, does a cold break never take place? A good deal of the gyle was transferred over with the wort, and ultimately clogged my CFC.

I did have an issue with my getto-rigged drain tube strainer (if you want to call it that) - I molded half of one of those herb / hop strainer balls around the inlet of the manifold (didn't work too well).

But I was thinking, even if my screen had worked better, would it still filter out the gyle? Doesn't the cold break tighten the cake on the bottom of the kettle? Also, what is the best filter to use for the drain tube in conjunction with a CFC?

You still get cold break, but it goes right into the fermenter with the wort. The best strainer out there I know of is the "Hop Stopper". I've never used one but they are nice. Instead I always just put a SS scrubbie over the end of the dip tube and that filters out the whole hops just fine. I've also used hop bags. I don't worry much about the cold/hot break getting into the fermenter, it all settles out.