I do think that homeless people have adequate access to health care. I think that the homeless people in this country actually have a great health care system. If they ever have any problem, they can get access to medical care in a free way. I think that the homeless shouldn't even get health care.
The current health care system is particularly poor in terms of long term treatment options for people with mental illnesses, whether those folks have homes or not. Therapy is limited and doctors are urged to prescribe medication but not spend much time helping the person learn more adaptive behaviors. A large proportion of the homeless population are people with mental illnesses. These diseases are poorly managed and, as a result, these people are far less functional than they could be. It's a tragic waste of lives.
Homeless people do not have adequate access to health care. Essentially they are left up to their own devices and left to the streets to die. People end up homeless for a number of different reasons but a large majority of them have mental problems. If they knew how to go about getting health care of it they could, they may not be homeless.
There is no segment of the population with less access to health care than is the homeless. I'm pretty sure the only time many of the homeless get to see a doctor is during a visit to the emergency room, by the time that has happened it can often be too late.