No, in order for it to be updated in every page request, you will need to manually refresh its pages, but that would be a bad idea.
LastActivityDate refers to the last activity in the membership provider domain, i.e. request authentication token, password to change, etc.
If you want to track the page request for each user, which will be a different domain, as usual, is used as a log file for all page requests for each user.
source
share