Yes, this can be done, binding to a property that you update with the desired value. I'd suggest you look into the MVVM pattern (Model-View-ViewModel), which is really useful for structuring this nicely working with WPF. Check out this video for a nice overview:
MVVM video
Using MMVM you would create a class which would be the ViewModel class. This one would typically be set to the DataContext of the View. Having done so you could add dynamic references to the other properties of the class, e.g. binding your text field to some property holding the Id og the ComplexObject. If your ViewModel class had a property ComplexObject, which again had a property ID you'd simply bind to the object like this:
<TextBlock Text="{Binding ComplexObject.ID}" />
Having this you could trigger creation of your ComplexObject from mouse click, which you should ideally set up as a command binding. Also note that the ViewModel class (or whoever is holding the ComplexObject needs to notify the View when the object has been set. This can either be done by making the ComplexObject a DependencyProperty or by making the class holding the property implement the INotifyPropertyChanged interface - giving it the PropertyChanged function to trigger the changed event. I prefer the latter.