As far as air goes, the factory box is pretty good as a cold air system, although the paper element restricts flow somewhat when driving in the rain (check your filter minder after a trip in the rain and you'll see what I mean), and the factory plumbing feeding the turbo is a gauntlet of accordians and baffles. That said, any restrictions in either the intake or exhaust side will contribute to turbo lag, which I felt was most noticeable to me having come from a 7. 3L Banks turbo'd Ford.
After mild intake upgrades (and a full exhaust), the turbo spools instantly and hits hard, even running the BDDL in stock mode. I use a cool blue hose to eliminate the factory airbox-to-turbo plumbing with an AFE PG7 drop-in. I can easily put the factory filter back in if I need to for service.