It would have many collisions with many shorter passwords.

But almost certainly not any collisions with very simple and very short passwords. The hash output space is sufficiently large.

Someone who (given infinite time) found a brute-force collision would likely find one of the shorter preimages first – you aren't really gaining anything by going ever-longer, after your preimage choice has as many bits as the hash output.

But if the attacker truly needed to brute-force it over the entire 160-bit (SHA1) or larger (other hashes) output space, unconstrained by usual simple-password-like limits on what to try as preimages, that's impractical, and you've achieved your goal... even if you overdid it on the input.