Yes. It is an “inside the Loop” global.
$page (int) The page of the post, as specified by the query var page.
It is setup and used by setup_postdata which executes at every iteration of a standard Loop. Though meant for use inside the Loop, the variable would still be set after the Loop to the last data it was given (unless specifically unset and I don’t think it is, but am not swearing to that).