The plan works (more or less) as Han gets his reward near the end of the film and little is made of it, beyond Luke needing to convince Han to help with the rescue by telling him the Princess is rich.
The version of the scene that exists in Star Wars: A New Hope that we all know Obi-Wan Kenobi gets Han Solo to take them on their journey by appealing to his greed.
Han never realizes Luke and Obi-Wan had to play him at the outset.
They offer him more money than he asked for, but less up front to get him to agree.