Esp. if you were running Windows, I would assume. I haven't seen that kind of propagation on non-MS platforms (just my observation).. I'd like to know if a browser on an Ubuntu box would be equally vulnerable - correct me if I am wrong.
Most drive-bys are targeting either old versions of IE, Java, Flash, or rarely Windows Explorer issues in XP.
Chrome is great because it auto-updates regularly, and auto-updates Flash. But even in Chrome I turn on Click-To-Play (since I need to have Java installed, and don't trust Java).