If the current system of hierarchy persists, then of course bitcoin could cause a greater divide between the rich and the poor, and us middleclassmen will be the ones who will be impacted most from this. Now, Bitcoin offers profitability regardless of how much you put in the system. Thus, this puts the rich and the poor on equal footing with respect to the chances in profits, Hopefully this is sufficient in whittling the current rich and poor people scenario most of us face right now.
If you think about it, the wealth would be not be distributed to poor but would be redistributed from those who hold stocks, real estate and fiat to those who hold lots of bitcoin. In essence nothing would change for average man but the FIAT rich would suffer the most.
A wise analysis, especially when we take into consideration the fact that bitcoin is independent to the fiat side of things. Still, we can't really expect the poorest of the poor to be able to invest in bitcoin, if only there is a subsidy program they can take in order to be able to taste the profits in bitcoin as well.