The answer is no.

It is easily shown that Ruth's father did not make the money he wanted.  All one must look at is the fact that he constantly moved his family around, because he could not make enough money being a rabbi to support his family.  So, without a doubt, he did not achieve that goal.

I do not believe that he achieved the goal of becoming an American, either.  Yes, he was an immigrant to the United States.  But being an American means something, and typically we think of that something as 'freedom.'  Being an American means freedom, and I do not think Ruth's father achieved any sort of American freedom.  He did not believe others deserved freedom, as shown in his strict adeherence to his religion and his unwillingness to accept his daughter as a Christian or her relationship with a black man.  He did not provide his family any emotional freedom or any physical freedom, as he beat them, belittled them, and worked them to the bone. I believe one cannot be an American without subscribing to the idea of freedom, and Ruth's father did not believe in freedom. So, no he did not achieve either of these goals.

In the book, The Color of Water, Ruth says that all her father wanted was money and to be American. Did he achieve those goals?

In the novel The Color of Water Ruth's life choices are deeply affected by her childhood and the attitudes of her father as well as the treatment she receives from her father.  She recognizes all her life that her Jewish faith separates her from the society a little bit.  She grew up in a time period of greater anti-Semitism than is seen today, yet she still had wonderful friendships outside the Jewish community.  Her father struggles with finding a place to settle in and bounces the family around as he loses various positions in various temples across the eastern seacoast states.  He is an American in the sense that he can freely practice his religion and that he can take whatever steps he wants to achieve financial and social success for his family, but his Jewishness and his bad behavior always leave him on the "outskirts" of whatever local community he lives in.  He runs his store and keeps kosher products for his customers, but he treats his customer's poorly and acts in ways that perpetuate negative stereotypes about Jewish business practices (ie. his attitudes about credit and pricing).  To answer your question, I think he would say he achieved his goals, but at what expense to his family's happiness and connectedness?  Ruth runs away from the family (at her mother's behest) as soon as she can and she ends up living a very fulfilling life as a Christian woman married to a black man in Harlem.  She couldn't have grown up to be any more different from her father if she has intentionally set out to do so, yet we see that Ruth lives a much more emotionally satisfying life as American.  She epitomizes the freedom and opportunity of what it is be American.