The answer to this question is necessarily a matter of opinion. There is no way to objectively determine whether hegemony as Gramsci conceives of it is actually at work in a given society at a given time. In this answer, I will describe Gramsci’s idea of hegemony, give arguments for and against the idea that it helps explain how states function today, and leave it to you to decide which side of the argument you find more compelling.
Gramsci’s idea of hegemony holds that the dominant class in any society does not simply use coercion to maintain its dominant status. Oppression through such means as police states or legal discrimination is not the only way that these classes remain dominant. Instead, the dominant class in a society maintains its control in part through what Gramsci calls hegemony. Hegemony is a process whereby the dominant class gets the other classes to “participate in their own oppression.” It does this by creating an intellectual and cultural climate in which the vast majority of people come to think that the current status quo is natural and valid. In other words, hegemony is the process by which almost everyone in a society (lower classes included) comes to think that it is normal and right for society to be the way that it is.
It is certainly possible to argue that hegemony continues to help states function in today’s world. In the United States, for example, inequality of wealth is at a very high level. There is a great deal of talk in some circles about how “the 1%” has too much of the wealth and too much of the power. Gramsci would point out that 1% of the people cannot hold down the other 99% unless the other 99% in some way agree to be held down. In the United States (one can argue) most of the 99% agrees to be held down because it buys into the rhetoric of capitalism and free enterprise. The 99% believes that it is right for the 1% to hold so much wealth and power because it believes that the 1% got that wealth and power through talent and hard work. Therefore, most Americans believe that their system is natural and normal and that people who do not have enough wealth and power should simply work harder. In this way, you can argue, the poor and the middle class in America participate in their own oppression, thus helping the state to function.
However, one can also argue that the social structures of given countries have nothing to do with hegemony. The main argument here is that a particular social structure exists because it is natural and normal. In this view, the US system functions because capitalism and democracy are the most logical systems of government for that place and time. The people are not being fooled when they think that their system is operating as it should be. The same would go, for example, for people in China who accept the domination of the communist party. In this view, political authoritarianism is simply the best way for that particular society to be run at this point in its history.
There is no way to objectively tell which of these points of view makes the most sense. It is up to each person to decide this question for him or herself.