If you're using the same account for all your customers and you're going to let it spread around, that's equivalent to not setting a password at all for that account (or to make it public), even if that's put inside your binary code. That's because it's de-facto impossible to keep control over a piece of reserved information that reaches more than 5 people, even if those are reliable, the systems they work with are not. If you really want to control who accesses your DB (as you should), keep the authentication on a restricted place, such as on the server side, as suggested above.
Regarding man-in-the-middle attacks, if you're going to communicate over unreliable networks (e.g., not your small LAN), you should assume this can happen (either to sniff SQL or any other type of information) and you should protect your communication, for instance by using encrypted connections (e.g., SSL or TLS). Unless, of course, you don't care what is sent around, or you accept a low-to-medium risk to be intercepted.