The question cannot be meaningfully answered as posed in the title of this piece, because "democratic" and "justice" are both subjective terms.
The influence of the laissez-faire economics of Adam Smith is still very strong in the US, with its notion that everything will be wonderful and all will live in abundance if only businesses are left alone to do as they see fit. "Laissez-faire" translates pretty much to "leave it alone," and "it" is business. Smith argues that if businessmen were just left alone to do what they do, an "invisible hand" will guide them to act to the benefit of mankind. Making their businesses more economically successful and creating a more just world with less squalor and poverty will be one and the same.
Amazingly, nearly two and a half centuries after Smith began to spread his ideas of the all-beneficent, all-curing invisible hand, people still behave as if it actually made sense, despite massive evidence to the contrary having accumulated in the meantime. In this as in so many things, it's impossible to know how many people really think it makes sense and how many say they do because they see a chance for personal gain. Ronald Reagan's plan of "trickle-down economics" is very Smithian: cut taxes, and cut social programs paid for by those taxes, and poor people will not suffer, because the resulting growth of the economy will benefit them more than the social programs did. In 1980, running against Reagan for President, George Bush Sr referred to the trickle-down idea as "voodoo economics;" later in 1980 he became Reagan's running mate and got on board with the Gipper's economic plan. People naturally assumed that Bush's criticism of trickle-down economics had been sincere, and that his apparent change of heart was a matter of political calculation, but in politics as in economics, who knows who's being sincere when, and for what what reason? Maybe Bush was in favor on trickle-down all along, and only criticized it in order to attack Reagan and try to win the nomination. Who knows.
For advocates of laissez-faire, trickle-down, liberatarian economics, taxes and government regulations concerning business are tyranny, they are un-democratic. For others -- let's call ourselves what we are: socialists. Let's stop being afraid of that word -- unrestricted businesses can be a prime source of tyranny, driving down wages, forming monopolies, fixing prices, profiteering from pollution and wars and other man-made catastrophes.
I'm a socialist, but I'm not asserting that every corporation is unmitigated evil. Mitt Romney was wrong, of course, when he said that corporations are people, but if what he meant to say was that individual people make up, control and operate businesses, and that these individual people can choose different ways of going about their business, and that therefore every business should be regarded as an individual case, just as every individual human being should be, then of course he was right. Still, by and large, over the course of the 2 and a half centuries since Smith, corporations have provided an immense amount of evidence that they should be watched carefully by governments, and regulated when necessary, because if Smith's invisible hand really does exist, if it's unregulated, much of the time it's giving most of us the finger, not looking out for us.
I say that many of us are socialists and should stop running from the term. That's because minimum wages, universal health insurance, regulations against pollution and against monopolies, universal education, universal nutrition and so forth are all socialistic. Like most of the rest of the countries on Earth since the US was founded, the US follows a combination of laissez-faire and socialistic policies, and there's a constant debate and power struggle between the 2 tendencies, which we also call conservative and liberal. Same thing. As long as you keep in mind that in most countries, "liberal" doesn't mean what it means in the US, it means "libertarian." One of many good reasons to call ourselves what we are, socialists, is to help Americans and non-Americans each understand what the other group is talking about.
To return to the title of this post: does democratic rule equal social justice? We will make more sense in our political debates, we will have a greater chance of getting along with each other, if we realize that we don't all define terms like "democratic" and "justice" in anywhere near the same way. And the example of how businesses are treated is just one way in which those terms are defined differently by different people. They're also applied in very different ways to issues of gender, ethnicity, freedom of speech, education, etc, etc. Some would say that I'm a moral relativist and that I'm attempting to thrown open a door to social, political, economic and other kinds of chaos. I would reply that, yes indeed, I am a moral relativist, and that all I'm trying to do is draw attention to the vast levels of chaos which already exist, chaos to which most people's eyes are stubbornly shut. Which is not surprising, it's a scary sight. Still I draw attention to it in the hope that seeing the chaos somewhat more clearly will be a beginning of a chance of reacting to it somewhat more effectively.