Yes, you can connect to your MySQL database remotely on our Linux servers. You will need to use a client such as:
MySQL Administrator: http://dev.mysql.com/downloads/administrator/
You will need to set up access using the Remote MySQL icon in the “Databases” icon group in your cPanel. Just enter your own IP address in the field beneath “Add Access Host.” If you don’t know your IP address, you can instead us a percent symbol (%) for “wildcard” access.
Additionally, you must create a database as well as a user and then add the user to the database prior to establishing a connection. Here is a link to an article that will walk you through that process:
When you connect, the hostname will be your domain name and the port is 3306.