In all cases, Internet Explorer using InPrivate doesn't store records of the visited URLs or the cookies of an InPrivate session on the disk. It does, however, store cached files (
.html files, images, videos..) of the InPrivate session, but it removes them when you close the browser. So we have two cases here
Shutting down before closing the browser: Browsing history will not be retrievable, but cached files will stay on the disk. Please note that in most cases, normal shutdown closes the opened applications and waits for them to close safely. Of course, it's different when there's a power failure or you use Sleep/Hibernate.
Shutting down after closing the browser: Browsing history and cached files will not be there, but it could be possible to retrieve cached files using data recovery methods.
For more information on what InPrivate stores on disk or memory, check the relevant pages by Microsoft for Internet Explorer 8 and Internet Explorer 9.
So in conclusion: It is possible for Encase to recover the cached files of your browsing session but not the browsing logs themselves (history of visited URLs).