If you're running your website off a Windows server and they provide a MySQL database for you - then yes they will (otherwise the MySQL database would be useless to ASP etc.).
If you're not running your website off a Windows server then it's really hit-and-miss, as the majority of Linux/Unix web hosting providers I've seen don't give you access to iODBC or UnixODBC.
The bottom line is - ask your hosting provider if you're unsure.
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