Yes.
This group is widely documented as "(self-)homeomorphism group of the Cantor set" (by Stone duality).
It admits, for every prime $p$ and $p$-adic field $K$, and $d\ge 2$, the group $\mathrm{PGL}_d(K)$ as a closed subgroup (viewed as acting on the projective space $\mathbb{P}^{d-1}(K)$ which is homeomorphic to a Cantor space), and this group contains a non-abelian free discrete subgroup.