It depends what you mean by “use ODBC.”
First, “Note: It is against our TOS [Terms of Service] to use our servers as database servers. Remote hosts should only be used for administration purposes only.”
That said, I’ve been able to connect to a Site5-hosted MySQL database from another machine using an ODBC driver, as a proof-of-concept for a client who wanted to do this on their own network.
From SiteAdmin > Databases > Remote MySQL, add the IP address from where you will be connecting.
Install the appropriate MySQL ODBC driver on the remote machine, and follow the driver’s documentation to build a connection string.
From Windows, you can use Control Panel > Administrative Tools > Data Sources (ODBC). I created a User DSN; it requires the IP address of your Site5 server and uses port 3306, as well as the database name, database username, and database password. I haven’t tried a System DSN or File DSN.
So, technically, yes. But note the Terms of Service, and there’s a perfectly good phpMyAdmin instance on your Site5 server for administration, so I’m not sure of the practical purpose.