Too early to say, but unlikely in my opinion. I expect VS code to continue to gain features and language support, one day we might even see a R# plugins for it but I don't expect it to bring Windows heavy features like WPF/xaml and Winforms across. Apparently C# and F# story on VS code is already pretty solid for server side apps
Visual Studio is written in C++ and C# and expects the Win32 API. Moving that to Linux would be a massive, many year project even for Microsoft. Will never happen. Instead something new like Visual Studio Code that is cross platform is more likely to continue development.