I recently migrated my Piwik installation from one server to another. As stated in the documentation, the installation process should be aware of the database when I'm using the same database name and prefix like in the other database.
But I only got presented with the choice to delete the found tables and not an option that I can reuse them.
When you migrate, you have to install the same Piwik software version. It's also easier to copy your existing config.ini.php and edit it for the new server.
However, if you install a newer version of Piwik with an older version of the db schema, Piwik doesn't offer to reuse because it expects more tables to be present. It's a bit of a catch22... the db update can't run without a config.ini.php.
In fact there was a bug, see: http://dev.piwik.org/trac/changeset/5024