Version 12.20 of Sprinter is the latest release. If your ALM server is compatible for this version, would recommend giving it a try as it will have the most up to date features (and supported items).
EXTJS is not specifically mentioned as supported in the HP Sprinter Product Availability Matrix. But they do make mention of some YUI, AJax and jQuery versions.
This document can be found here: [PAM]
If you have an avenue with HP to be able to file a support ticket, I would suggest doing so. The functional support team (Sprinter and UFT) can more directly answer for you as to what is explicitly supported vs maybe partially or not even at all.
I know from past experience they will take enhancement requests for Sprinter on suggested supported technologies. I have filed JSON and jQuery ER's myself in the past.