I don’t think so, because only Trent and Peggy have access to the Secret that’s at the base of the first hashes. Since that Secret is a component of the hashes that are given to Victor, the algorithm allows him to get from the proof hash to the encrypted age hash just by hashing the proof 18 times.
It’s important to remember that the secret really has to be secret between just those two or else, yeah, there’s a weakness there similar to what you describe. If Sally is 20, then this happens:
Sally and Trent share a secret and hash Sally’s age minus eighteen plus one, so three hashes. This is the proof
Sally then uses the secret to hash her age plus one (21 times). Of course, just as before, the difference between the number of hashes remains eighteen, plus the hash of the secret.
Problem is Victor starts with the hash of three, and hashes eighteen times for 21. His seventeenth hash will match Peggy’s age.
Over the course of the night, Victor would now know the order of the hashes and therefore know how old people are relative to each other, and statistically be quite likely to figure out what the hash for exactly 18 is since it’ll be very common and none will lead to it but many will be just above).
The secret being, well, secret, prevents this.