Current password hash functions will not just add the salt before hashing, instead they do a lot of iterations and use the salt in each iteration. So you cannot just do it the other way round.
Actually what you have in mind is to generate a key out of the user password. There are functions which where created exactly for this purpose, they are called key-derivation functions. Well-known key-derivation functions are BCrypt and PBKDF2 (Password Based Key Derivation Function 2).
So in your case you would store the hash of the password in the database for authentication, but use a different salt to generate the key for encryption. This salt you have to store somewhere too, but not the key itself.