If I construct a class in AppScript and add a method, is it possible to get the autocomplete feature to work when I type a period after an instance of that class?
Unfortunately jsdoc only works at the top function level in apps script, so methods declared with this.method = function() {} neither show up in the generated docs nor in autocomplete. It sucks, but there it is.
You could join others in starring this this apps script issue
But it's been open for almost 2 years now, and I don't see any movement on it.