A personal thought about this, already many people don't know how to safely send a regular string to the database... let alone sending a password.
That being said, MYSQL has a PASSWORD() function that you can use to save a password in a string. Pretty close to what you're talking about.
Most languages now have extensions that will hash the password and give you a string to save in the database. They may even have a compare function so you don't have to do much to know whether a password entered by the user is a match.
In terms of security, I think the main issue is that you often open your database without encryption. So hashing the password beforehand is safer. Having encryption on your database connection is also going to slow down the queries. Everything will have to encrypted/decrypted before it gets transferred.