Very possible, with liquid fueled systems, too. Solid fuel rockets don't handle damage well, either, but that is usually apparent early in the trajectory.
A multi-stage missile is going to have obvious weak points being transported horizontally, as they do. That's why the Saturn V and Space Shuttle used the Crawler Transporter in the vertical position. Ideally, a multi-stage ICBM should be siloed, assembled on site, and fueled prior to launch. They cannot remain fueled for long, since the chemical composition is corrosive to the missile parts in long-term storage. The Norks seem to be reluctant to silo, because they know they'd be priority targets.
