Comment from Art on this functionality:
"jQuery UI does provide a hook for the drag start event. So, we can definitely add this feature.
The only thing to consider is that since this event fires when the user starts dragging an element, and it's very likely that the user will still be dragging the element when the response comes back, there might be some minor usability issues if the response modifies the component being dragged or the draggable object itself, like losing the grip of the element. We fixed a similar situation in slider, so we might be able to fix this situation for draggables as well, if we make some necessary changes in the rendering. However, in some cases it may depend on how the component being dragged is rendered. "
(Restricted to icesoft-internal-developers group)

I estimate this can take half a day (4 hours) to implement, test, and also to analyze different situations that can arise with this feature like the one described in the first comment.
(Restricted to icesoft-internal-developers group)

Committed feature to the trunk at revision at 32526.

Added 'dragStartListener' attribute and 'start' ajax event, as well as a 'datasource' attribute to fetch data when working with draggables in UIData components.

There was a problem when using helper="clone". Since a clone node is created from the original node, the id attribute is not included (otherwise it would be duplicate), so when retrieving the id from the clone node, during the dragStart event, it was undefined and it wasn't possible to determine which node had been dragged.

Committed fix for this problem at revision 32852 to avoid relying on the id of the clone node, but on the target id specified initially.