I'd like to answer this question by side-stepping some of the questions about caste and race.
The core part of this question is whether someone who would usually be considered "socially disadvantaged" might be able to escape this "disadvantaged" status if they have acquired wealth.
To answer this question, I'll draw on the framework of "social capital" and "cultural capital" from Pierre Bourdieu. These other two types of "capital" exist alongside "financial capital" - which of course, is money and wealth.
In general, in a "capitalist-esque" society, they would escape some of this disadvantage, but not all of it. In this framework, financial capital can be converted into social or cultural capital by purchasing things like housing, clothing, education, training in etiquette, and so on. These would increase a persons social standing and prestige via an increase in "cultural capital". Things like education and training can be purchased - e.g. if I am rich enough, I can become well educated and learn to speak in a well mannered way, and thereby be respected by other well educated people.
However some things cannot be purchased (for most normal people).
For example, someone who uses a wheelchair can still only access areas of the country which have accessible pathing. Even if they were very wealthy, this limitation would still exist, and this would constitute a social inequality. In the above framework - being a wheelchair user costs a certain amount of social capital - because "society" itself may not highly value your ability to move around and access things safely and easily. But this is a norm which is slowly changing around the world.
Another aspect of social inequality would come from a marginalised group's relationship with the law. If you are part of a group who is forbidden by law to do certain things (for example, imagine a nation which forbids women to work) - then even if one is wealthy, they are still affected by that social inequality. However access to wealth would allow them to move away to another part of the world.
These arguments however, can always be countered with "but what if I had even more money? I would simply spend money to change social norms or improve the social and physical infrastructure so that I would no longer be marginalised."
That is correct as well.