Sure can, among other things.
The BOV causes the car to run rich, since metered air is exhaust to the atmosphere. The corresponding metered fuel however is sent to the engine. So during a rich situation, unburnt fuel is sent out the exhaust. The fuel can foul spark plugs, the vanes of the turbo, the O2 sensor, and even the catalytic. Any of these can cause awful performance from the car, stalling, hesitation, and most likely CE lights.
If you're running one, I'd recommend removing it for a BPV, either the stock TT valve, or an aftermarket, Forge or Bailey. Check your spark plugs for fouling. They'd be a real dark color. Normal is a very light brown, almost reddish color. Check your O2 sensor, and have your catalytic checked, it could be plugged solid.