Adding callback function for wp_ajax_ has no effect

Yes. It is possible and you’re on the right track! 🙂

AJAX calls happen “behind the scenes” and no screen output is generated during the process no matter what you echo or print_r – that’s why you don’t see anything returned to you – instead that server response is captured by javascript and acted upon there.

That gives you two basic options for debugging your AJAX actions:

1) You can use error_log() in your AJAX actions to write the output to WP_DEBUG_LOG file and check the results there:

function darn(){
     error_log( print_r($_POST, 1) );
     exit;
}

For more details see Codex: Debugging_in_WordPress – WP_DEBUG_LOG

Pro-tip #1: Fire up a terminal console and use tail -f debug.log for a live stream of debugging awesomness 😉

Pro-tip #2: Use tail -f debug.log | grep -v 'bad-plugin' to filter out too much debugging awesomness from plugin authors who don’t use WP_DEBUG_LOG ;P

2) Use javascript’s own console.log() to check the response right in your browser:

Send a response from the AJAX action…

function darn(){
    echo 'darn!'
    exit;
}

… and receive it with JS:

$.post(ajaxurl, data, function(response) {
    // Response will be 'darn!'
    if( typeof(console) == 'object' ) console.log( response );
});

Pro-tip #3: Instead of simply echoing the response like we did above you can use wp_send_json() for generating a JSON formatted response or WP_Ajax_Response class for a XML. Handy for more complex responses and/or error handling!

Pro-tip #4: Let me know in comments if anything remains unclear 😀

Welcome and have a great time on WPSE!