Apparently not in complete generality; here is a a formula for a <A HREF="http://homeweb.unifr.ch/jacquemm/pub/docs/Inradius.pdf">hyperbolic truncated $n$-simplex</A>, and here for a <A HREF="http://link.springer.com/article/10.1007/BF00773406">regular simplex</A>. There is also a formula for a triangle.