Could an extremely wealthy person get out of an arrest this way?

Of course someone might get out of an arrest this way. It's called a bribe and happens all the time. As far as not taking a bribe, there are plenty of honest cops out there that would not take the bribe simply for the fact that they have a decent amount of self-respect and a good amount of respect for the law. Keep in mind... if you accept a bribe, you are breaking the law as well.