The answer is yes and it worked but the offer was a 3 hour booking, not "extra" for one hour which in most cases means nothing. In the case of an in demand MP who worked a limited schedule, I would offer a higher guaranteed tip than what she is used to and she would take an appointment on a day she wasn't scheduled. The caveat is she knew me.
If the girl does not know you or the agency doesn't know you and you have no credibility credit, so to speak, such offers tend to mean shit. All of the above is common sense.