Will mixed mode assemblies (C++/CLI projects) work on .NET Core?

Unmanaged code in context of C++/CLI is always platform specific and is compiled for a specific OS (Windows) and specific CPU architecture (x86/x64). Unmanaged code in C++/CLI ends up being much like actual C++ code compiled using a C++ compiler. Since mixed mode assemblies can contain native code, they are bound to a specific OS and CPU architecture.

EDIT (March 2019): This answer predates .Net Core and may be out of date in Core context.

Whether or not a mixed mode assembly works with .NET Core is not determined by platform specific code. Support for mixed mode assemblies is being worked on in:

https://github.com/dotnet/coreclr/issues/18013

As far as I understand this will require recompiling C++/CLI projects to target .NET Core.

Of course, a mixed mode assembly with x86 code for Windows will only work as x86 in Windows and so on.