No, Classic Shell doesn't do anything to affect Explorer's ability to remember or restore folder view settings.
However, Explorer in Windows 7/8 *should* remember the View settings by default. You might find this article helpful to understand how Explorer stores it settings:
http://winaero.com/blog/how-to-set-a-fo ... rge-icons/ Depending on the folder contents, there are 5 templates involved and you must set the view settings for each template (Documents, Pictures, Music, Videos and General) separately.
If your folder views aren't remembered despite setting them for each template, you might find this freebie useful:
http://free-sk.t-com.hr/T800soft/softwa ... ptions.htm It forces Explorer to use the older view control which behaves differently (and may remember settings for you).
Also, as you observed correctly, Libraries override the folder's view settings and use their own rules. They apply the parent view of the Library to all folders inside it when accessing the folder from inside the Library. There is no way around that other than opening the folder directly (without accessing it via the Library).