Short answer: maybe.
It all depends on how the content in your existing MySQL database was structured. If the old content was created by a content management system, see if it has a built-in exporter. WordPress has plug-ins that can import from a variety of commonly-used CMS platforms already. Check to see if yours is supported.
Unfortunately, if your content was just kind of "there" in the database without a CMS or any kind of standard (non-custom) structure, then this won't really work. My recommendation would be to use phpMyAdmin to export your content, then use a text editor to cut out the portions you want to keep and manually create new blog posts within WordPress. This process will be very time consuming but can be optimized if you want to build a custom importer.