From a client machine, it is unlikely that your database information can be sniffed. However, if your application "leaks" information, it is possible for an outsider to get sensitive information about your database. For example, if you have the CustomErrors parameter set to "Off", and your database is inaccessible for any reason, users may see your database's address and can then proceed to attack it using brute force or known exploits. There are other ways you can leak sensitive information this is just one example.
In general, it is not ideal to have your database open to the internet -- it is generally advised that your database be behind one (or two in case of a DMZ) firewalls. If you can control this, you should move it somewhere more secure. Or else even without your application leaking its address, a port scanning "war dialer" will eventually find it and alert the "bad guys" to its existence.