Interesting theory. This movie has elves at Santa's workshop lurking around the city possibly all year long while disguised as regular kids to determine the Naugthy/nice kids to report to Santa.
No.
https://www.countryliving.com/life/kids-pets/a34981398/elf-on-the-shelf-story/
This movie predates the Elf on the Shelf, but I also agree that this movie is unlikely to have inspired the writer of Elf/Shelf.
We never had one for our kids, but the people I know who did were also the type of parents who didn't have a really good handle on raising kids and controlling obnoxious behavior. By making the Elf the heavy who would report children's bad behavior to Santa, it gets crappy parents off the hook - "if you don't behave, the Elf will tell Santa!!". And no, I don't mean every parent who had one was like this, but a lot of them did use it that way.