What I do similar is,
Pw_hash = hash('f4/$$er3@' + salt + plain_text_pw);
If the attacker only gets the database (which has the hash and the salt) and not the source code they don't have the 'f4/$$er3@' value needed to perform any attacks
Your approach offers effectively zero additional security; it is trying to add "features" to salting that don't work towards their actual purpose.
Edit: If you want to have something site-wide that an attacker wouldn't have while decrypting an offline password database, the thing you're looking for is an encryption key.
The only redeeming factor I suppose would be that you have to store your random string somewhere anyway, at least this method required code traversal rather than just an SQL field named "password_salt".