NO absoloutly fix the airbox, TTS tuned my GSX years back and they ALWAYS use the airbox where possible. That means anything upto and generally including race prep they only junk it when its either too restrictive which you would be surprised to find how far an engine can be tuned before that happens. Or the engine mods require big induction mods like turbo's and such, like drag bikes with nitros , Or the bloke paying the bills say's so, Pod filters only work efficiently at flat out.
The airbox acts as a buffer to pressure waves caused by wind, riding at speed and the reflections off of the carbs themselves (the same tuning that affects an exhaust affects the carbs)etc and give a pool of calm balanced air that can be fed evenly to all cylinders at an even if not low temperature and pressure. It is also much better at protecting the motor from dust, water and general crap. The greater part of the crap a motor sucks in is rubber and that really messes with the internals.
By all means fit a K+N element as that will give much better airflow but keep the airbox if even remotely possible.
Your bike really will thank you.