First, I doubt it will be implemented. I am not aware that Stack Exchange is doing something like this for any other language. A comparable feature might be useful to other languages as well, and this might justify the effort on the side of Stack Exchange. However, from a technical point of view this means doing things the wrong way. Normally it's the responsibility of the operating system to handle keyboards and other input methods. The specific conditions that make it useful to detract from that only exist for Esperanto. Therefore it would ultimately be an expensive feature just for one site. So long as it is still in closed beta and it's not at all clear whether it will satisfy the general demands on activity (and can do so in the long run!), this question is really premature.
So far most questions and answers are in English, not Esperanto. I am not very optimistic that this will change when we reach the public beta stage. Even when entering a question in Esperanto with only a few words or a citation in English it would be very annoying when you have to correct words such as aŭiliary - which is currently what you get when you set lernu.net's dictionary to "English -> Esperanto" and type in
auxiliary. (To get the expected result, you must type
auxxiliary or switch off the 'x' method.) So this feature would at least require a button for switching it off quickly.
All in all, I think this real problem should better be addressed on the user's side. This question prompted me to finally do this for myself. As a Firefox user I immediately found the Transliterator add-on, which solves the problem nicely. Presumably, similar plugins exist for the other major browsers.
Hints for Firefox users:
The 'Transliterator' plugin does the job. The Esperanto-specific Firefox add-ons don't - they only change the display of existing content that is 'x' method encoded. After a quick installation that didn't even require a restart, plus configuring Transliterator for Esperanto (I believe the default was Russian), I can now activate the 'x' method by pressing F2. I just did so, which made the input field for this answer get a blue border and activated the 'x' method. The 'xx' escape doesn't work, so to type auxiliary, I must either deactivate the Transliterator plugin by pressing F2, or type something like
auu[Backspace]xiliary to separate the keystrokes
By the way, this add-on also makes it easier for users to clean up other users' 'x' encoded texts. Just select the text you want to convert and press Ctrl-Shift-Q. For me this doesn't work because in my browser, this combination is already taken by a different plugin and I did not allow Transliterator to override it.