Yes, it is possible, but it depends on what you do.
You can't directly call a PHP method from JavaScript, but you can run an action in a controller class as follows:
Code:
core.post(
URLHandler.buildURL({target: 'example', action: 'test'}),
function(XMLHttpRequest, textStatus, data, valid) {
}
);
This will run
\Xlite\Controller\[current-area]\Example::doActionTest().
Please could you explain the desired behavior in details?