I know this thread is a bit old, but I just joined the site and figured I'd drop a reply in case you were still wondering about this. It's very possible that a woofer could be blown without the tweeter getting taken out too. Tweeters tend to be somewhat protected by the manufacturers from audio extremes because they are delicate and would blow easily. High frequencies also aren't near as demanding on the mechanics as low frequencies are. I'm dealing with this myself on my G6, with two blown front door woofers but the tweeters are ok.
In my car, I'm most likely going to convert to a set of coaxials or maybe components with tweeters located near the woofer. Whatever the case, I'm going to just flat disconnect the factory tweeters when I get at it. Factory equipment usually sounds dull compared to quality aftermarket stuff, so leaving the factory tweeter would just hurt overall sound quality.