We'll let others debate the veracity of that argument. But there appears to be one major reason the rich would get better political outcomes than the poor: They participate in the political process more. Much, much more.
And it's not just in campaign donations, which of course are going to favor the wealthy who have disposable income to give to candidates. The nation's poorest also vote at much lower levels than its richest, and generally aren't as politically inclined. And the poorer you are, the less involved you are.
Courtesy of Pew, here's the political participation rates of people relative to how financially secure they are (broken down into five categories):
These numbers are pretty remarkable. While 63 percent of the most financially secure Americans were likely voters in the 2014 election, just 20 percent of the least financially secure were. And the decline in voting frequency is consistent as you get less and less financially secure. In fact, the decline on each of these measures is consistent as you move along (and down) the financial spectrum.
This is why Democrats are the party of voter-registration drives. They know that non-voters are much more likely to favor Democrats. And that's especially true of the least-financially secure non-voters, whom Pew found favored Democrats 42-17 in 2014.
Despite that lopsided margin, however, the vast majority of that 42 percent weren't likely voters, which means Democrats won far fewer votes from the least financially secure Americans than they could have. If the party got those people to vote as often as rich people (and Republicans), they would probably be the dominant American political party.
Warren's supporters might argue that poorer people don't participate in the process precisely because they're frustrated with how rigged the system is. But the lack of participation by the poorest Americans is striking. The question is whether someone like Warren can possibly make a difference on that front.
There are certainly plenty of people who could be receptive to her message; they just might not vote for her — or even be registered to do so.