For now, older MySQL sites will continue to function, and the behaviors for the MySQL functionality are still available in Dreamweaver, although in the latest DW versions, you need to install the deprecated server behaviors extension.
In the future, when PHP 6 is released, the MySQL libraries will not be available, and at some point Adobe will no longer make the deprecated server behaviors extension available, that is where the MySQLi extension comes in.
Realistically, older sites using MySQL will work for as long as your host gives you the option to use PHP 5 on the server. to put this into perspective, I use 1 and 1 for hosting. in my control panel i can select to use php 4 or php 5 on my site.
So as long as you can use php 5 on your server and have a version of dreamweaver that has the MySQL extensions, your old sites will still be fine.
There is no one step conversion of old site to MySQLi, they would need to be recreated. That is not something that needs to be done tomorrow, but it is something you should be thinking about long term.