No, it's not. .net is more than .net core, and it's not 100% open, nor cross-platform.
The long term plan from what I've read is for .Net Core to eventually form the foundation of the .Net Framework, then the Framework (Windows/GDI+/COM+/etc) libraries with be built on top with other OS-specific libraries being created for other platforms.
The vast majority of the .Net framework is already Open Source[1] including the compiler[2]. What in particular are you missing that you need?
[0] https://blogs.msdn.microsoft.com/dotnet/2017/01/19/net-core-...