Let $R$ be a ring, let $A$ be an Azumaya algebra over $R$, does its topological Hochschild homology coincide with that of $R$? For example, let $\mathbb{H}$ be the quaternion algebra over real numbers $\mathbb{R}$. Then what are $THH\mathbb(\mathbb{H})$ and $THH\mathbb(\mathbb{R})$？

(I learned that the usual Hochschild homology of $R$ and $A$ coincides, and wondered if the topological version detects the Brauer class.)