Mick,
Yep.
Basically, the air flow runs something like this:-
Atmospheric air (1 bar) goes through the air filter dustbin & along the corrugated hose to the Turbo.
Passing through the turbo it is pressurised to ~1.6 bar, and goes back through the lower pipe (sort of parallel to the corrugated one) and out of sight to the intercooler.
The intercooler is like a radiator / oil cooler thingy with the big hose going into it one end.
As the pressurised air goes through the radiator, it is cooled by airflow (like coolant in the normal radiator), and becomes more dense.
At the other end of the intercooler, it goes into the metal hose which comes back out through the wing (with a nice new grommet!). It then goes through the last big bore rubber (or stainless, or carbon fibre) hose (the one where you fit a ‘dump’ valve – if you have one) to the throttle body where it mixes with petrol and into the engine (simplified version!).
As such, the metal pipe should be attached to the outlet from the intercooler radiator. If it isn’t you’ll have no turbo advantage as the engine is only sucking in atmospheric air!!!!!