That's really what it comes down to - people brought up in the middle to upper class are tought about delaying instant gratification throughout their formative years, whereas the poor are often exposed to the pursuit of instant gratification, by way of drugs or crime, or laziness.
And this is where your argument falls apart.
It's not WHAT you know, it's ...
From what I have seen, successful people succeed not because they fuck up less, but because when they do fuck up, they have a STRONG NETWORK OF SUPPORT to catch them. Consider two dudes who sat around on a Monday smoking Kools and watching Judge Judy -- Abel and Buster. Abel had a wife who, while definitely disgusted with him, was the daughter of a psychologist, and decided to take the approach of probing Abel to see what the source of his depression was. After a long session of talking, fueled by some wholesome, protein-rich food made by Abel's sister, who was a good cook and visited often, they decided Abel should have a long talk with his old classmate from school, who himself had fought a bout of depression and kicked a smoking habit with the help of Zen meditation. Not only did Abel's friend cheer him up, he even gave him a couple of leads to some good places that were hiring for some rather interesting jobs.
Buster had married the girl he got pregnant. She'd dropped out of school and ran away from a mother who beat her. Her only friends were people who could relate to her -- similar young women who'd known nothing but pain and depravation from day one. So when her husband Buster sat around, she had no resources to fall back on, nothing to think of that would give her hope for him. So she simply nags him. And he lights up another Kool.
The only way to break the cycle is compassion. You can BE THAT PERSON who inspires a disaffected person to say to themselves, 'You know, I am worth it, and I owe it to myself to do better than I'm doing.' Simply being friends / acquaintances / coworkers with a person who's positive and forward-moving can be all it takes to motivate somebody onto the right track. I'm hardly advocating you let the disaffected leech off of you. On the contrary, it's the little kindnesses that get the ball rolling.
Back to the original question, at the time of writing this, no, not every poor healthy adult has the human / cultural capital to better themselves. But it doesn't need to be like this, if the haves show the have-nots a bit more respect and inclusion.
less mouths to feed = more money for stuff. 
They are the necessary counterpart to profit at the top.
