Adding skills to the database is very easy. In fact creating new races, professions, cultures, talents, statistics, spells, training packages, monsters, etc... it is all quite simple to do with AutoHARP.
Now the init system in the combat tracker is hard coded and it definitely isn't ceats. It's straight out of the book. Creating an action/turn based system could certainly be possible but that would have to be coded. Interesting idea for an enhancement. I don't think I would outright program ceats, but it would be very easy for me to associate a table to the actions that already exist.
AutoHARP uses wxWidgets and C++. It doesn't have anything where a person could input a PHP or Javascript program that could be used to implement a new combat system. That is another interesting idea, however that will be a complex task. Not sure how I would do it. It would require some thought. The action/turn initiative is far easier to write.