The root of the problem is, that the ol3 click handler is executed before the handler you are trying to add, so probably the best way is to remove the original click listener before adding your own.
Because the ol3 listener is added by Closure library, it cannot be removed with jQuery and is unnecessarily complicated to be removed with vanilla JS, so your safest bet is to just remove all listeners on the element. This can be done by the following (a bit hacky, but I don't know a better alternative) piece of code (see Remove All Event Listeners of Specific Type):
var btn = document.querySelector('.ol-attribution button');
var btnClone = btn.cloneNode(true);
btn.parentNode.replaceChild(btnClone, btn);
Fiddle: http://jsfiddle.net/Kenny806/ds9em02a/
Another way is to collapse the attribution as soon as it expands, so from user's point of view, nothing happens. A (bit clumsy, but hopefully readable) fiddle here: http://jsfiddle.net/Kenny806/udpdohqg/1/
It works a bit unreliably in the fiddle, but works fine in my modified version of ol3 attribution example.