This is a complicated question.
TL;DR: Democracy may include some elements of hegemony to a varying degree, assuming you use some sort of Gramscian (leadership) or Marxist (effective power of unequal input into decisions being made) definition.
Let's look at two angles:
First of all, democracy and hegemony are not necessarily 100% mutually exclusive - you can exercise some forms of hegemony even in nominally "democratic" systems, even ideal "direct democracy" as envisioned by theoretical political philosophers.
While nominally, everyone has a chance to input into the decisons via the vote, in practice almost no "democratic" system lets everyone vote.
Voting itself is not nearly as important in the political ecosystem as convincing other people in the rightness of your opinions so they vote the way you want them to. As such:
In any direct "townhall type" political activities, those with big biceps and in generally aggressive psychology and intimidating looks get unequally large chance of having their ideas promoted, by physically intimidating their opponents from speaking against them. Double extra for smaller communities where the threats can be of implied "we know where you live and where your kid goes to school" type.
NOTE: This is not a theoretical example. A convicted left wing terrorist Brett Kimberlin has very recently successfully attacked several conservative bloggers in USA by methods ranging from "innocent" filing of frivolous lawsuits, to extremely dangerous and life-threatening practice of "SWATting" - placing a fake emergency phone call tricking 911 operators into dispatching emergency response teams to a targeted person’s home. Some more details here.
In 2016 elections (and in 2017), Trump supporters were physically assaulted on multiple occasions; and at least one campaign rally had to be cancelled due to security threats.
Even more importantly, people with high talent for persuading others (because of high verbal IQ, rhetorical training or talent, or simply good ability to lie convincingly) get unequally large chance of having their ideas promoted.
A related type of this is people with ability to mass-communicate (which requires both a physical platform AND an established cultural trust).
Wikipedia article hegemony cites that in contemporary society, the exemplar hegemonic organizations are ... mass communications media that continually transmit data and information to the public (I omitted the churches as that is no longer true in most Western countries).
E.g., a Politics.SE user - no matter how cogent and smart - gets a lot less political influence than a random New York Times hack. And a guy without a blog or SE account or other such platform gets even less influence than someone with one.
Also, people with a lot of resources can hire and pay professionals who are good at either persuading others, OR intimidating others, to unequalize the system in favor of their ideas (See, {Soros|Koch} - pick one according to your biases).
Secondly, In practice, in virtually any modern political system larger than a certain threshold, "direct democracy" discussed above is not even feasible, and is instead replaced by what is known as "representative democracy".
The difference is that, in direct democracy, by definition, everyone has a chance to equally influence the outcome of any decision.
In representative democracy, everyone has a chance to equally influence the outcome an election for a representative, but only those representatives have a chance to influence the outcome of decisions (with certain rare minor caveats like referendums).
This results in even more possibilities for hegemony, such as:
Elected political class has a complete hegemony in USA (shared with government bureaucracy).
They not only hold monopoly on legislative decisions, they also form a nearly insulated class. You don't get to become one of them unless they as a class approve of you - which typically strongly transcends political labels.
Yes, purely theoretically, everyone (with caveats) gets a vote for their representative.
But most people don't really get much of a choice for who to vote, nor much of an input into how those they voted for/against decide when they make legislative decisions.
Incumbency re-election rate fluctuates between 80-90% in most national congress races.
Many races are essentially formalities (e.g. it really doesn't matter who gets nominated/runs/wins in Republican primaries in many areas of NYC - the winner of DNC primary is 100% assured to be elected. Same is true in reverse in red states.
Witness whole political dynasties - from Kennedies to Bushes to Clintons just to list the high level visible ones.
People who had unequal opportunities in convincing others in direct democracies to vote for ideas (see the first half of the answer), ALSO have the same exact unequal opportunities in convincing others to vote for their preferred representatives.
To top that off, people who wish to have unequal input into decisions being made can now influence representatives in non-electoral ways, from lobbying, to corruption, to open quid-pro-qua, to more stealthy "you get to work for us as a highly paid consultant when you retire" stealth quit-pro-qua.
To your comment, thanks for the clarification. I think cultural hegemony is an invisible political power. Correct me if I am wrong.
– L'Unità Jun 25 '13 at 06:29