Definitely a cat stuck in your engine bay somewhere.
But it really sounds like a leak of some sort. Doubt it's a line popped off, but rather a leak at a connection that is somewhat close together, sort of like putting a blade of grass between your fingers and blowing through it.
I would guess: bpv gasket, intercooler-throttle body connection (those rubber ends tend to pop off and leak like that), or turbo-intercooler connection.
If it was a line popped off the manifold to the bpv it would idle like dookie and your bpv wouldn't work and you'd get compresssor surge.