Definitely not. The back-end takes a user's password and hashes it with that user's specific salt. Then the result must be in the table. Another user's password will not work.

What you are worried about is a result existing in the table, even with the wrong password. That can only happen if you have a hash collision. The article on collisions I cited (http://preshing.com/20110504/hash-collision-probabilities) says that even with 171 trillion hashes already IN the database, the likelihood of a collision is still only 1 in 10^18. And that's using SHA1 -- SHA-256 would be even better.

[Edit] Ooops, I forgot a zero. It's actually 1,710 trillion hashes in the database to make the risk of collision 1 in 10^18. OK, that's 1.71 quadrillion.