I do know this for sure. There are ways to find out how many pieces the page file is in and I've seen Windows Vista / 7 / 8 that after a year or three were in hundreds and thousands of pieces and after doing the procedure I outlined and moving the page file to a partition in front of the boot partition and making it all one piece the increase in speed was noticeable.
Sorry, I'm not wrong at all. The automatic Windows defrag utility can not defrag the page file anymore than any third party software can, the page file is opened very early in the Windows startup process and once it's opened it can't be moved or defraged, the PageDefrag utility written by Mark Russinovich for Windows XP included a driver that started before almost all other processes and services and it was able to defrag the pagefile before Windows opened it but it was very limited in that it could only move the pagefile to available continuous space and if there wasn't enough continuous space for the whole thing it would do it's best to consolidate how many pieces the file was in but it could not move other files to make enough continuous space for the pagefile. Also every time you did it (this is if you had your pagefile set to automatically managed) it would keep pushing the page file farther and farther towards the end of the disk (in order to find enough continuous space) and the farther towards the end it got the slower access to it got.
The utilities that come with Windows and the Windows auto defrag that was introduced with Windows 7 do a bare bones basic job, one of the best defragers I've ever used is MyDefrag and it does a really great job, better in many cases than commercial software.