I don’t know what you mean with text based module.
But shortcodes (or the code they parse) is just that code. If that code is responsive or has CSS styles that do responsive stuff that’ll work just fine.
If your theme doesn’t allow for that, that’s a shortcoming in the theme then 🙁
In AdRotate Pro you can use the Mobile feature yes. That’s different from responsive as you simply create a ‘normal’ advert and then a 2nd one that’s smaller (thus optimised for mobile screens).
See the manual in my previous post for more info on how that works.