Take an arbitrary holomorphic map $f\colon\Delta^{*}\to\Gamma\backslash D$, which extends to a map to a toroidal compactification of $\Gamma\backslash D$. Then $f$ also extends to a map $\Delta\to\overline{\Gamma\backslash D}^{\rm Sat,\tau_{ad}}$ where $0$ is sent to a point with rational coordinates, i.e., a point in the dense subset $(C(F)\cap U(F)\otimes\mathbb{Q})/\mathbb{Q}_{>0}\subset C(F)/\mathbb{R}_{>0}$.