I am thinking about writing a WPF User Control for my application. I am using MVVM in my application.
User control\'s may require Dependency Properties that can be
A UserControl is part of the "View" in "MVVM" just like the TextBox or ListView controls are part of the View.
Whether you decide to use MVVM to develop your UserControl itself or write it in QBASIC (not recommended) it does not break the MVVM pattern for the consumers of your UserControl so long as they can do every thing they need with your UserControl by binding to DependencyProperty's exposed on your UserControl. i.e. Your UserControl should expose the properties it is dependent upon (hence the name). Once you grasp this DependencyProperty's suddenly make a whole lot of sense and you want their helpful on changed event handlers and default values you specify in their constructor.
If your UserControl is in a different assembly or not I cannot see how that makes a difference.
That said many would advocate you build your UserControl using the MVVM pattern itself for all the good reasons MVVM brings e.g. helping another developer looking at your code. However some things simply are not possible and/or much harder more complex and less performant hacking the XAML to do this - I am not talking about your garden variety Add User Form but for example a UserControl handling the layout of thousands of visuals. Furthermore since you are working in your View you do NOT want your UserControl's ViewModels mixed in with you applications!
Basically I am saying it is well within MVVM not to use MVVM on your View!