From what I've seen, the answer is yes. Build once, drop and run anywhere.
.Net Standard is just an API specification which will be implemented on the .NET Framework, .NET Core, or Xamarin runtimes. Technically it's a subset of the .NET Framework libraries. It's more of an improvement on .NET Core as it is bringing more APIs to that runtime.
So basically as long as you use the APIs in .NET Standard, your application can be compiled for any of those 3 runtimes.