Yes.
Yes. The issue with including something like this in the core API is that every request has to pay the thread safety price even if they don't use it.
This is a bit harder to do in the general case. With Servlet you could just create a thread safe wrapper, where the wrapper basically disconnects from the underlying request on timeout. The Undertow native API is not designed around wrapping though, so it needs cooperation from the application to manage this.
If you know the application is only going to be writing data (and not setting headers) then you should be able to make this work via a ConduitFactory implementation that handles the locking, although if this is not the case then you are going to need some kind of external lock.
Stuart