The answer seems to be a big NO, at least not without doing some kind of plugin.
This is an issue raised alot on the ExtJs forums as well, citing the same issue I have which is that you don't always know what text is going to be used for the Label. i.e. Internationalization.
This is an expensive process to perform client-side and could/would affect rendering times. It would be much better to try and calculate an approximate width on the server and set the LabelWidth property.
We might be able to implement client-side calculation in a future release. I think it would be a handy feature to have, although it's going to take time to develop and test.*
I'm moving this thread to the Feature Requests forums so we can better track the request.*