I ended up moving the functionality of LoadModels()
to another class that implements IStartupDataLoader
and then I was able to test it like this
// Arrange
var sdl = A.Fake<IStartupDataLoader>();
var exp = A.Fake<ObservableCollection<Model>>();
A.CallTo(() => sdl.LoadModels()).Returns(exp);
var sut = new MainViewModel(sdl);
// Act
sut.Loaded();
// Assert
Assert.That(exp == sut.Models);