I had an H2 back in '72 and the hot tip was to take off the airbox top, because the intake horn on the top of it was very restrictive. The horn was there to quiet down the intake noise, which was really noticable when the cover was removed, but the power was much better. On the modern bikes, like the CBR's and RC51's, the only real restrictions in the intake tract are the flapper valves, which are there also, to lower the noise from the intake and the paper element OEM air cleaners, which are somewhat restrictive as well. Removing the flapper valves, upgrading the air cleaner to a higher flow after-market item or upgrading the the air box to a higher volume item will see an improvement in performance for a modern bike.
Leave the cover alone.
'12 KTM RC8
Bazzaz GP Quick Shift
Rottweiler Ram Air
LadyBird Full Titanium HRC Replica Exhaust
Lockhart CF Frame and Swingarm Sliders
Galfer Superbike Brake Lines
Turn One C/F Snorkle & Airbox With K&N Filter
Turn One Radiator Ducts w/Spal Pusher fans
Samco Radiator Hoses
Powdercoated OEM Wheels
'11 CBR1000RR Repsol Edition
'65 CB77 Vintage Road Racer