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At least, that generally sums up what I've seen across a universe of quite a few site overhauls.
caveat - you will likely see a short-term dip in your rankings as the engines re-index your site. Don't worry. If your work is solid then you will see the rebound as well. If not, get in there and review what you've done for obvious errors - like redirects on any URLs that you've retired.
If it's just design changed, my experience is it depends on the before/after code.
One thing that could potentially affect you: if you're moving to a theme that substantially changes the internal linking structure of the site with big navigation changes or the like. (some themes come with plugins/widgets to do this type of thing - mostly beneficial results, though)
LisaB