First of all, every stored password should be hashed with a different pseudo-random salt. Second, SHA-256 is not appropriate for storing passwords; instead, you want to use a key stretching algorithm, as has already been mentioned. There is a lot more detail at Crackstation.
An encrypted hash is also called a keyed hash, and the key is sometimes called a "pepper." There need not be a separate encryption step. Instead, the secret key is part of the input to the hash function. That can improve security somewhat. There are two ways attackers can get a copy of your password hashes. One is to compromise the storage mechanism, as with SQL injection. In that case, a keyed hash can make it effectively impossible to retrieve plaintext passwords from the hashes because the key can be compiled in to a program or otherwise kept outside the password storage mechanism. The other way is to compromise the OS itself. In that case, the key is compromised, and is no longer an impediment against attempts to attack the passwords.
So, the short answer is yes, but you have to do the underlying work right, first.