Not only is it possible to use Sencha Touch and still have all of the QuickConnect JavaScript calls available for your application but it takes only a few minutes to get everything going.
Ed Canas has graciously created a video of how to do this. In the video he creates a QC application from the iPhone Hybrid template and then embeds the Sencha Kitchen Sink demo. He also shows how you can make your iPhone app compile for the iPad.
All of this in 7 minutes.