Nowhere does it say you must install W3TC. If you don’t want to, simply don’t use it.
But then also, don’t use the caching support option in AdRotate (Pro).
If you’re not using ‘disk basic’ then fragmented caching in W3TC probably won’t work correctly. But that’s a bit trial and error to see what works for you.
AdRotate is not capable of removing scrollbars. If it’s gone after placing stuff on your site then probably there is a conflict with an advert you use and your theme. Or one of your adverts has a issue (missing closing tag for example) that causes the scroll bar to be gone. However, having a custom scrollbar controlled by your theme is a bigger issue i’d say 😉