smcmahon's answer truly helped my company get this going, and now we are doing this regularly - developing the front end using GWT and the backend with .NET/MS technologies.
I've been a MS developer my whole life - latest silverlight frontend with .net backend. it took about a month worth of work but finally we implemented a smooth process to develop single page GWT apps in Eclipse, using .NET backend/web services developed in visual studio 2010. On the .NET side we receive/transfer all objects in JSON rather than XML (we use Newtonsoft JSON generator because .NET default JSON generation from WCF web services gave problems, especially with dates). On the GWT side we use overlay types.
We wrote an app which generates code (from the .NET app) and automatically writes it to our GWT project - it generates all classes that we need and also writes functions for easy calls to the web services. On top of this, we were able to get the .NET web services functioning while we run the app in GWT, which makes it WAY easy to debug. then when we are done with project changes, we compile to javascript/html - copy that to visual studio, and deploy our project. couldn't be simpler.
It took a lot of work to figure all this out with the help of this thread, but was TOTALLY worth it once we did since we are a straight microsoft shop with SQL server backend and IIS windows servers. Silverlight was great, but now we are moving to the point where staff are getting pads and need to run apps on their phones as well.
We use UIBinder for the interface. Love the GUI designer/xml declarative layout, and modularity. Can still use any HTML/CSS we want by having the UiBinder HTML panels in the UI. The uiBinder designer even recognizes CSS3 tags and renders them better than IE9 does.
GWT was a great solution, and Java was very easy to learn coming from a C# background.