Absolutely, however you might run into a few problems.
Assuming you have a login, make sure that your login has permission to login from a remote host. In the USER table from the MYSQL database, are three important columns: host, user, and password. You need to make certain that your account is in that table and that the host column isn't localhost. You can wildcard the host column with a value of "%". This would allow your user account to login from any IP. However, it would be best to put in your static IP some someone can't hack the SQL server.
Also, you might want to check and make sure that the SQL server is even communicating with the outside world. By default SQL communicates TCP/IP on port 3306. So try this:
"telnet ip_of_sql_server 3306"
If you get a bunch of high ascii, then the SQL server is communicating with the outside world. If you get a timeout then there is a firewall blocking that port or SQL is running on a port other than 3306, which you have to find out.
There is a whole permission based system that is pretty robust and secure for MySQL and you can learn more about it by going to the MySQL homepage and reading the documentation
