[dgacmu]

No - per the definition of a trapdoor function: "For any k ∈ K, without trapdoor tk, for any PPT algorithm, the probability to correctly invert fk (i.e., given fk(x), find a pre-image x' such that fk(x' ) = fk(x)) is negligible"

https://en.wikipedia.org/wiki/Trapdoor_function

Note that the definition is about a pre-image, not necessarily the input used to create it in the first place.

Second, that definition is absolutely not correct. "Never" would require that the size of the output of the hash function be equivalent to the size of the universe of possible inputs, which it obviously isn't. There's a very important difference between "never be observed in practice" and "never, period." You're not using the language precisely, and that's very dangerous when talking about hashing and cryptography.

[AstralStorm]

Pre-image is even simpler. A good cryptographic hash also prevents second pre-image attack e.g. pre-image based on multiple hashes.

None of those properties is needed for indexing into hash table. Good collision resistance is all that is required and salting for more paranoid cases.