Visitor groups based on visits under a root page

you can sure do that if you want.  you will need to track them via an http cookie, profile setting, or via dds.  Totally up to you.  What you will need to do is climb the tree until you hit the specific page and then set the value if they have visited the specific page or its subpages.  But yes, this is totally do-able

You could also use the category criteria to accomplish this out of the box. If the subpage has the same category as the root page. You could also create a custom criteria that check in the IsMatch function if the page they are visiting has a parent of the selected type.