In general - that is most likely true. But there are differences and there are differences. I think relationship between wealth and status is not straightforwardly linear, but at least heteroschedastic or even qualitatively different in different ranges.
Most likely that relationship follows the S-curve. In the low range (say between $50k and $500k) social status trumps wealth. That is, a high status person is more likely to get a more prestigious and a better paying job than a low status person, regardless of their wealth. In the middle range (say between $0.5m and $10m or so) wealth is the key factor determining the social status of the person. But in the high range, the effect of wealth follows the law of diminishing returns, and the social status again trumps wealth in determining a person's access to resources.
To illustrate:
A white male is more likely to get a relatively better paid waiting job in a five star restaurant than a Latina woman.
Ceteris, paribus, a professional Latina woman worth, say, $10m is more likely to get a job in a prestigious law firm than an Anglo woman worth $300k and most likely am Anglo male worth as much (albeit gender may still trump wealth in some instances).
A corporate exec worth $20m with the right social status (and thus capital) is more likely to get a high profile government or corporate position than an executive worth $60m but with "wrong" set of social attributes. In fact social status buying is an important motive in corporate philanthropy.
Another thought:
When I was in a grad school, I conducted an experimental study (for my qualifying paper) testing the effects of ascribed social status (gender) and human capital (education and job experience) on the perceived job qualifications (basically, a hundred+ Rs evaluated resumes that varied along these dimensions). I found that gender had no effect on perceived qualifications for the highly educated applicants with substantial work experience, but being male had a strong positive effect (i.e. males were judged better qualified than females) for candidates without education and long work experience.
That seems to suggest another relationship between wealth and status - what money is for the rich man, social status is for the poor man. That is to say, the rich are judged by their bank accounts, the poor and not-so-wealthy - by their social status.
Wojtek