If you are talking about using this approach to beat down prices, The "walk-up" strategy can work in SOME of the Islands, OFF-Season (May or October).... you walk up and say do you have a room, and the hotelier says yes, and you ask, what does it cost? And the hotelier says, €40, and you say, I can only pay €35 and you start to walk away... then maybe he might say, uh, I do have one room at €35.
I would not think it would work in Athens. At least the price-cutting part of it would NEVER work in September -- because a City like Athens gets MORE busy in september... Greeks are back from holiday, conventions are opening, and all the convention attenders are booking rooms, there are performances and athletic events bringing people to town ... Athens hotels are more full in September than in August. You may find a room (perhaps in a less desirable location) without booking in advance, but less likely to be able to negotiate price.