as far as I know, no, there's no such thing for Illustrator.
Also, not everything you can do in an Action can be done with a script (a typical solution for that is to run a script that runs the action).
Do jsx script developers more commonly invoke saved actions from jsx (how?) or invoke applescript (which can invoke menus) from jsx?
app.doScript("Change Water Color", "MapActions");
The first variable in the function is the name of the action that you are trying to call. The second variable is the action set that the action belongs to. Both are case sensitive.
AppleScript is able to script many things in the GUI.
The problem is it becomes version specific when they move stuff about.
CS6 can evoke some menus but is limited to those with keyboard shortcuts.
CS6 also got action calls added... ( to JS )
No nothing like action manager code exists in AI. ( a big shame )
PS has a plug-in to record your steps...
Giving you access to a whole range of app features beyond the regular DOM.
Only today X has posted that that he's hanging up his boots here...
That is unfortunate...Another great loss