It is possible, but not recommended. The problem is that angular does not execute the method in the ng-click directive as is (like in regular onclick), but instead evaluates expressions using the $parse service. From the angular doc:
Angular does not use JavaScript's eval() to evaluate expressions.
Instead Angular's $parse service processes these expressions.
The implementation of expression evaluation in Angular is deliberately forgiving.
In JavaScript, trying to evaluate undefined properties generates ReferenceError or TypeError. In Angular, expression evaluation is forgiving to undefined and null. It makes more sense to show nothing than to throw an exception if a is undefined (perhaps we are waiting for the server response, and it will become defined soon). If expression evaluation wasn't forgiving we'd have to write bindings that clutter the code
So the $parseProvider will not execute an undefined function at all, instead it will execute a noop function (which is an implementation of a null object pattern). Here is an excerpt from the $parseFunctionCall method:
var fn = fnGetter(scope, locals, context) || noop;
The execution of a null object will do nothing, and that is what's happening. You could probably achieve what you want by modifying the $parseFunctionCall to execute any function, instead of executing a noop function.
Changing code looks like the only option since configuration of these services is not sufficient for your use-case. However, i don't think it's a recommended approach unless you know the Angular API very well.
For additional reading:
Angular expressions
$parse service
undefinedfunction by substituting them withangular.noop