Yes. We can! Just now!
Try my demo application and learn how it works.

Source in GitHub: https://github.com/kostysh/Drag-Drop...r-Sencha-Touch

Screenshot_2012-08-06-04-45-21.pngScreenshot_2012-08-06-04-46-08.png

Some things inside Ext.ux.util.Droppable may seems strange.
This is because I have not enough information about the Sencha Touch architecture.
Maybe something can be implemented easier and better. Do not hesitate to tell me - how.