A catch can slows it down. It does not stop it.
Why the carbon builds: on the FSI and early TSI EA888 (Mk5 2.0 FSI, Mk6 and early Mk7 TSI) fuel is sprayed straight into the cylinder, so it never washes the back of the intake valves, and the oil vapour from the crankcase bakes onto them.
What a catch can does: it cuts the oil vapour reaching the valves, so the rate drops.
What matters as much: a healthy PCV. A failed one dumps far more oil mist than a good one, catch can or not.
What you still plan for: a walnut blast. I pull the intake manifold and media-blast the valves with crushed walnut shell through a vacuum shroud. It is the only real clean, and chemical intake cleaners do not touch carbon baked behind a closed valve. I treat it as maintenance every 60 to 80k miles on a direct-injection GTI, not a one-off repair.
One exception: engines that add port injection alongside direct injection (some Mk7.5 and Mk8) largely solved this by washing the valves again.