It's the 'some period of time' that is always the worry.
We converted a well ranked local CPA website from home rolled html to WordPress earlier this year. We chose to wait until after tax season due to the fear of redesigning the site in their busy season.
I think we relaunched on May 1st, and there was no significant drop in ranking at any time. We 301'd everything that mattered to their new locations, and spent a few weeks chasing down links to get them updated.