I had a K&N replacement filter fitted to my E46 320d and it ran without any problems at all.
I fitted it when the car had reached 19000 miles (first oil service). I was astounded at how dirty the OEM filter was and my dealer said that it wouldn't be replaced until 60000 miles!
The engine would be starved of air by then. My neighbour has an E46 330i Clubsport and has found the same amount of dirt at 15000 miles.
I don't know if it was the K&N filter or just the fact that I replaced the dirty filter, but performance did improve and my fuel consumption improved by about 10% as a result
. From our experience, if you want to maintain max airflow, replace your filter more regularly than the service schedule recommends i.e. at the first oil service.