It depends on your nation and your make-up. In a multi-ethnic empire, then your anarchists are going to be the oppressed minorities, yes. Sometimes, they follow the philosophy of anarchism. Sometimes they are people who want the central government to just have less power. Really, they can be, and usually are, a grab bag of various groups that are opposed to the current government, are banding together to end it, and have no major political bend.
As an example for someone like Russia for example, Anarchists and Socialists both want to overthrow the government, and they both may rebel. If they rebel, the Anarchists and Socialists may work together, but the Anarchist faction in this scenario would likely have few, if any Socialists because those Socialists looking to rebel are already in the Socialist faction.
But yes, the Anarchist faction can go a variety of different ways if they are able to succeed. It's a bit of a catch-all unfortunately, but just look at them as people who are really not happy right now