You could probably re-purpose some parts of the Wordpress template by replacing Wordpress code with the relevant Mezzanine code; but this approach seems much more work-intensive than simply adapting your Mezzanine project to match the look and feel of the Wordpress site. Also: you'll need to do something about your existing Wordpress data; there is a method for importing Wordpress into Mezzanine (
http://mezzanine.readthedocs.org/en/latest/blog-importing.html), though I have not used it. As for basic help with templates, look here:
http://rosslaird.com/blog/customizing-mezzanine/.
I suppose the short answer to your question is "no" -- you won't be able to use a Wordpress template and have everything just work. Mezzanine and Wordpress are completely different systems and built with completely different code. You'll either have to adapt your Wordpress template (ripping out all the PHP code and other WP-related stuff, replacing it with Mezzanine code) or rebuild the template completely.
Cheers.
Ross