This forum has many reports of both success and failure in migrations like this. My personal experience has been heavily in the area of success, especially when other changes are not made at the same time as the CMS change.
The biggest problems people run into are when they get complicated. If you maintain technical precision (especially in redirects if the URLs change), maintain essentially the same internal navigation, and don't make other changes at the same time (for instance, "trimming content"), the odds of success are very good.
This thread from July 2010 calls out a lot of the important technical factors:
Site Relaunch Checklist [webmasterworld.com]