Although the warranty may not cover you, the frame is HIGHLY unlikely to be incapable of supporting you, and yes, Specialized definitely has published limits. As fietsbob already mentioned, the wheels are generally the weak link. Either ride the stockers till they fail or proactively upgrade your wheels to something sturdy (not terribly expensive either) and ride your heart out.

I've ridden with more than a few 300 lb+ dudes on this very forum who have road bikes and they're doing just fine. They even ride those flimsy road bikes up mountains, so don't limit yourself.