There are some challenges.
Local data storage
Swing applications can use the disk to store data. Assuming local data store available in HTML 5 works, it'd still be difficult to auto-magically map file/disk access to local data store calls.
Multithreading & Synchronization
Swing applications typically create threads, and that's not possible with GWT. Tricky to get it right.
Network Access
Swing apps can connect to arbitrary network locations, which doesn't work with GWT.
Using java language features not available in browser
Anything outside core-java is inaccessible, so the automatic port will likely fail.
Memory & Performance optimizations
Garbage Collection patterns are entirely different. How do you optimize for optimal download sizes? How do you map multiple swing screens to use something like code-splitting for performance gains?
Look and Feel
All said and done, you have to get your hands dirty to write some CSS code to get the right look and feel. An automatic port cannot do that.
Given all this, I think it is not-possible for anything but trivial applications. And for trivial applications you might as well re-write the code.