Is a brat a switch?

Usually not. A brat is typically on the following side and resists on purpose, because being caught is more fun than going along quietly. A switch genuinely moves between leading and following.

The confusion comes from how brat play looks. A brat is arguing, refusing, running, so from outside it can read as a struggle over who's in charge. Inside, both people usually know exactly who is going to win.

Some people are both, and a switch who brats from the bottom is a common combination. But bratting on its own says nothing about which side you prefer.