On one hand, it's kind of a tautology - sure, if you're in a city that is very car-dependent, it's a disadvantage to the working poor because owning a car costs money.
But in the US there are also (usually older) cities with relatively great public transportation that are more walkable that also have enormous amounts of wealth inequality.
Doesn't really have anything to do with inequality, in the US at least it's mostly just reflective of when cities were built and developed. Pre-WWII cities like NYC and Boston have (again, relatively) great public transit options and huge walkable parts, while newer cities (often in the South) developed around the car.
On the flip side, Boston is the only city where I've ever hit a car with my bike.
https://www.nytimes.com/2015/05/07/upshot/transportation-eme...
An example of such would be Atlanta, where public transit investments have been sparse due to wealthier areas of the metro having little interest in funding transit. Many wealthier residents live suburban developments that are highly car dependent. As the article points with walking, many wealthier areas opt to avoid transit access, many residential areas do without sidewalks and follow a land use pattern that (effectively) cuts the neighborhood off from pedestrian access
Europe may have great biking culture and equality, but they have effectively sacrificed pluralism.
In places where the working poor are the most disadvantaged, there also tends to be the highest auto dependency. (Think American South, Panama City, Panama etc)
To Soap box for a moment, almost all of our problems are reflective of our vast inequality. Our ability to live more sustainably, enjoy greater opportunity, ability to form new businesses, household formations, civic function etc. ultimately are limited by the degree of inequality a nation faces.