To me, being good is a function of altruism, while being bad is a function of egoism. This starts to get whacky when you do an altruistic thing for egoistic motives (ie donating for recognition) but it serves me as a baseline, and by that understanding, I would say yes, theoretically it is possible. However, in most scenarios I can think of, the way that a person becomes rich will be filled with egoistical decisions and thus be bad.
I am currently re-reading pedagogy of the oppressed by Freire though, and he brings up a good point: charity and being charitable will always lead to an unjust system, because the person feeing charitable, to be able to do that, needs to perpetuate a system in which they have more, and where there is a poor one to give to. So he would say not really because the being rich in and of itself is a symptom of an amoral system. And I have to say that's a good point