Is it possible to use ajax inside the html output of a computed field?
Well, it's not Crashing with a white screen. You are using ajax_deliver which returns the content of your response as plain text and stops further page rendering.

A Crash would be a WSOD and no output. Check your hook_menu definition and be sure its setup as a non-menu item ... just a callback. You do this by setting the type in the $items array. You may also want to set the delivery callback value to be an ajax response.

Lastly, your link goes to hello_world_link_callback/ajax/, but that is not the URL you have defined in your hook_menu function. It may be a best-fit match for Drupal on a lookup.... but I doubt it.