One of the important parts of the disenfranchisement of the poorer class through the denial of basic health care is a relatively simple one. When you know that you cannot afford to see a doctor and your only avenue of getting some access to the system is the emergency room, there is no such thing as preventative care and it adds to the feeling of disenfranchisement as well as the dangers of constant illness, etc. that were mentioned in the previous post.
Those of us lucky enough to have insurance also have to learn how to navigate the system and get what we need out of a very flawed set up but we learn these things through experience and often with at least some help from the system.
For people completely shut out of it, everything about it is alien and it represents nothing but difficulty and the chances of being bankrupt because of an accident where a wound gets infected, etc.
There is no scientifically provable answer here -- this is more of a matter of opinion.
To me, the connection is that a lack of adequate health care can make the poorer classes more likely to remain in poverty. The reason for this is that the poor may be less likely to get good health care and so they will not be as healthy as the rest of the members of society. If they are less healthy they will, for example, have a harder time keeping a job because they might have to miss more work because they are sick.
Similarly, their children might miss more school because of being more chronically sick. If they are constantly sick, they will have a harder time learning even when they are in school. This will hold them back and make them more likely to be poorer once they are adults.