Random thought (not my field), length is still correlated right? Since these are public pages, could you infer with good probability url visited based on the transferred data size? (yeah gzip and stuff but you can compare gzipped)
If yes then especially for an active (participating) user I suppose you can take some good guesses.
This has been shown by security researchers to be quite possible, and a serious vulnerability in many popular web applications. Not only could pages be guessed, they can build an entire state machine of the web application and use side channel attacks to guess what a user is sending in their HTTP requests.
Yes, you could. It'd be a gamble but it's possible. This is why you should consider implementing length hiding[1], either via a header or HTML comment.
If yes then especially for an active (participating) user I suppose you can take some good guesses.