Yes, you can simulate a mouse click by creating an event and dispatching it:
function click(x,y){
var ev = document.createEvent("MouseEvent");
var el = document.elementFromPoint(x,y);
ev.initMouseEvent(
"click",
true /* bubble */, true /* cancelable */,
window, null,
x, y, 0, 0, /* coordinates */
false, false, false, false, /* modifier keys */
0 /*left*/, null
);
el.dispatchEvent(ev);
}
Beware of using the click method on an element -- it is widely implemented but not standard and will fail in e.g. PhantomJS. I assume jQuery's implemention of .click() does the right thing but have not confirmed.