I see that your question is quite old, but I solved it
All you need to do is trigger the mousedown event on the endpoint.canvas element, this will start the connector drag.
Of course the mouse won't be in the same place for the start drag, and the dragging doesn't actually start until the mousemove event, so I added little cheeky adjust on document.mousemove. There probably is a better way to do this, but this might be a good starting point for other people.
$(function() {
jsPlumb.ready(function() {
var jsp = jsPlumb.getInstance();
jsp.draggable($("#start"));
jsp.draggable($("#end"));
var endpoint = jsp.addEndpoint($("#start"), {
isSource:true
});
jsp.addEndpoint($("#end"), {
isTarget:true
});
$("#dragbutton").bind("mousedown", function(e) {
$(document).bind("mousemove.adjust", function(e) {
var left = e.offsetX;
var top = e.offsetY;
$(endpoint.canvas).css({"left":left, "top":top});
$(document).unbind("mousemove.adjust");
});
$(endpoint.canvas).trigger(e)
})
})
})