I fear that this is one of those "for your own good" features, but I'm wondering whether or not there is a setting in Firefox or Chrome (or perhaps Windows in general) that will allow me to recapture the scroll bar even though the browser may be busy.

I run into this a lot, especially when I have a lot of tabs open in either browser, and so perhaps it's just a fact of life. I wouldn't mind being able to scroll along gradually, even if the page hasn't had time to fully render all of the images, etc., yet.

Does such an advanced setting exist "under the hood"?