is asynchronous version of relaycommand required in order to run async methods correctly

1) Does RelayCommand need to be replaced with an asynchronous version (RelayCommandAsync)?

It doesn't have to be, but you should consider it.

2) What exactly is the current code doing regarding asynchrony?

It's creating an async void lambda. This is problematic because async void does not handle exceptions particularly nicely. If you do use RelayCommand with asynchronous code, then you'll definitely want to use a try/catch like the one in your code.

3) What if anything could/should I change to improve/correct it?

If this is the only async command in your code, I'd say it's fine. However, if you find that you have several async commands in your application with similar semantics, then you should consider writing a RelayCommandAsync.

There is no standard pattern (yet); I outline a few different approaches in an MSDN article. Personally, at the very least I define an IAsyncCommand in my applications, which I expose from my VMs (it's difficult to unit test an async ICommand).

However, what does not work correctly is the canExecute predicate functionality that automatically enables/disables the control binding to the command.

Assuming that RelayCommand.CanExecuteChanged is delegating to CommandManager, then you can just call CommandManager.InvalidateRequerySuggested after setting IsBusy.

Does RelayCommand need to be replaced with an asynchronous version (RelayCommandAsync)?

No, RelayCommand will work as desired here.

What exactly is the current code doing regarding asynchrony?

What happenes is that when overload resolution kicks in at compile time, it chooses the overload that takes an Action, which means your method is translated into async void and that is why your code compiles.

3) What if anything could/should I change to improve/correct it?

There are implementations of async delegate commands. You can find one here. One important thing to note is exception handling. In the case of an unhandeled exception inside an async ICommand which is bound to a WPF control, the exception would propogate to the binder and go unhandeled and unnoticed.

I don't think you need an async version of relay command. Your implementation looks OK. Does it work?

If you want to test whether the body is running async, add an await task.delay(20000) and see if the UI remains responsive whilst the command is running.