Yes, you can connect to your MySQL database remotely using a client such as MySQL-Front at http://www.mysqlfront.de or MySQL Administrator at http://dev.mysql.com/downloads/administrator/
Please remember to enter your own IP address or % for a wildcard in the Access Hosts area in Cpanel's MySQL databases.
Additionally, you must create a database as well as a user and then add the user to the database prior to establishing a connection. Your database name and username will be Cpanelusername_databasename and Cpanelusername_databaseuser respectively. The password will be the password for the user you created. The hostname should be your domain name. The port is 3306