Would be Drupal a good choice for my web app?
Both codeigniter and drupal are php frameworks. Can you elaborate more on what exactly you are looking for? Drupal is capable of doing everything a php can do. Also Drupal 7 has built in ajax support for forms. With additional modules like ctools, you can extend ajax functionality to any DOM elements.

There is Rules module that is more powerful and extended version of triggers. Its the GUI version of if-else-then php statements.