No.. It is the way in which Windows and the NTFS filing system works that brings about fragmentation.
The page file is not one file into which Windows stuffs bits that it doesn't need at that moment. It is a space allocation in a partition and page file data is not stored contiguously any more than the registry is one file in just one location.
You will notice that most articles about page file defragmentation are all about NT/2000 ending at XP, and there is next to nothing re Vista, Windows 7 and 8. I believe this to be a better ability by Windows file indexing to cope with fragmented files and
general improvements in file management.
I have been encouraging 25% free space for years now, been derided a lot for doing so because it is seen by many as a waste of HDD space, but the main reason for Windows slowing down over time is partly down to the free space on a new installation slowly
being eaten up.
I don't have a drive/partition with less than 44% free space available, and if it drops below 30%, I increase the size of the partition, replacing the drive for something larger if there is no longer space that I can pinch from other partitions on the drive,
or installing another drive to spread the load. And no, I am not made of money by any stretch of the imagination and have to be careful about what I do.. :-)
Ever since I read the Late Alex Nichol's s article on the Windows page file, the definitive guide of its time, I have taken an interest in how it works. That original article still holds good for some of its content, but we have to take on board improvements
which have been made since then, and not keep applying old tools and ideas to technology as it is today..