Does WPF databinding marshall changes to the UI Thread?

Yes for scalars, no for collections. For collections, you’ll need a specialized collection that marshals for you, or manually marshal to the UI thread yourself via the Dispatcher.

You may have read that INotifyCollectionChanged.CollectionChanged must fire on the UI thread, because it’s simply not true of INotifyPropertyChanged.PropertyChanged. Below is a very simple example that proves WPF marshals property changes for you.

Window1.xaml.cs:

using System.ComponentModel;
using System.Threading;
using System.Windows;

namespace WpfApplication1
{
    public partial class Window1 : Window
    {
        private CustomerViewModel _customerViewModel;

        public Window1()
        {
            InitializeComponent();
            _customerViewModel = new CustomerViewModel();
            DataContext = _customerViewModel;

            var thread = new Thread((ThreadStart)delegate
            {
                while (true)
                {
                    Thread.Sleep(2000);
                    //look ma - no marshalling!
                    _customerViewModel.Name += "Appended";
                    _customerViewModel.Address.Line1 += "Appended";
                }
            });

            thread.Start();
        }
    }

    public abstract class ViewModel : INotifyPropertyChanged
    {
        public event PropertyChangedEventHandler PropertyChanged;

        protected void OnPropertyChanged(string propertyName)
        {
            var handler = PropertyChanged;

            if (handler != null)
            {
                handler(this, new PropertyChangedEventArgs(propertyName));
            }
        }
    }

    public class CustomerViewModel : ViewModel
    {
        private string _name;
        private AddressViewModel _address = new AddressViewModel();

        public string Name
        {
            get { return _name; }
            set
            {
                if (_name != value)
                {
                    _name = value;
                    OnPropertyChanged("Name");
                }
            }
        }

        public AddressViewModel Address
        {
            get { return _address; }
        }
    }

    public class AddressViewModel : ViewModel
    {
        private string _line1;

        public string Line1
        {
            get { return _line1; }
            set
            {
                if (_line1 != value)
                {
                    _line1 = value;
                    OnPropertyChanged("Line1");
                }
            }
        }
    }
}

Window1.xaml:

<Window x:Class="WpfApplication1.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1" Height="300" Width="300">
    <StackPanel>
        <TextBox Text="{Binding Name}"/>
        <TextBox Text="{Binding Address.Line1}"/>
    </StackPanel>
</Window>