I've used Arquillian alongside with standard
JUnit tests in a recent project and I found it quite helpful when it comes to working out the initial skeleton of the web application, just as described in the book
Growing Object-Oriented Software, Guided by Tests. Arquillian seems to ideally fit into this kind of testing as it let's you build and test archives on-the-fly and defer final implementations of interfaces to a later phase when you're confident that the API is sensible.
One thing that Arquillian couldn't protect us from, were the errors that cropped out during actual implementation of APIs and frontend/backend integration but that's mainly because our infrastructure is not capable of providing full, proper testing environment (with databases, LDAPs, etc.) yet.
On the other hand, providing frontend developers with "fake" Arquillian web application archives made it possible to parallelize the work on frontend and backend. Which was a very good thing IMHO. :-)