If you think that Vaadin works similar as dekstop app you are wrong. Read chapters from about Vaadin architecure once again. Vaadin simplifies creation of the RIA apps, but not release you from issues like: mem usage per user, network usage, avoid sluggish ui, browser sandbox, etc
Porting application from desktop to web is complex task. You can’t copy and do some changes in class to Vaadin requirements. It’s not work that way.
You asking about porting VAADIN to .NET. IMHO it’s not possible due ASP .NET and Servlet API have fundamental differences and almost all DOTNET web solutions based on ASP.