Parts of it. Stuff like WinForms and System.Web are so wrapped around the axle of Windows that they probably won't be open-sourced, but a lot of it has been.
Winforms is fairly windows centric, but iirc there is a Mono compatability for most of the interfaces... as to System.Web, I'm pretty sure this has been open since ASP.Net v3, which iirc is included with Mono.
I haven't tracked Mono & .Net as closely for the past few years as I've been doing far more node dev, and/or migrating away from .Net apps.