It's not impossible. I've always interpreted the UI patterns as something intrinsic about their character and unable to be changed. If anything, it's the pattern of the recursion marking them. However, if any of the mythical ended up being a fake-out, it would be the one that arrived with Hermes.
The problem is it would make a lot of the writing come off as plot-driven rather than character-driven. Robert functions both as an insight into Asterion's makeup as well as a means to showcase humanity and how similar he is to the MC, at least as far as whatever makes a soul is concerned. It would be odd for that to be written off. I do think Robert likely has some twists for us. He just very casually switches from vacation away from important job in an extreme version of hell to a full-time hotel worker. His role as a guest/employee is more important than whatever details aren't given to us, but since every other character who has joined has gotten some individual spotlight prior, it's "of note".
However, like the shed being a secret quest, he could just be Minotaur Hotel's version of an optional party member. It's hard to say when you only have to juggle between Asterion, Luke, and Robert for spending free time. When more character side stories are available that balance may well shift.