I would argue that it does both.
In a way capitalism and democracy are very well-suited to coexist. Both capitalism and democracy emphasize the idea that people should choose their own ways and should have a great deal of freedom. Since both systems emphasize freedom and personal choice, they go very well together.
There is also a way in which capitalism can undermine democracy. This is because capitalism tends to cause inequality whereas democracy depends to some extent on having all members of a society be relatively equal to one another. Capitalism tends to cause situations in which some people are much richer than others. When this happens, democracy can be to some extent imperiled because the rich and the poor will have different levels of power. In addition, they may feel a great deal of enimity for each other and class warfare might erupt. Both of these are bad for democracy.
So, while democracy and capitalism can go together very well, they can also clash with one another.