I think so. I would guess it depends how fast you are going, I wear a full face motorcycle helmet. I am not fast enough to require a suit or cage.
Be sure to check that snell sticker on you old helmet because NHRA rules for 2009 state that "any car running 14.00 and quicker in the 1/4 mile requires a Snell 2005 or newer OR SFI 41.1A helmet (see complete list below)". Also a new NHRA rule in 2008 requires that "any car running 9.99 or quicker in the 1/4 mile requires an NHRA approved FULL face helmet with visor.