No, they didn't. I am on an android and having trouble searching. But they apparently popularized a particular image of Santa. Off the top of my head, Santa is originally based on a real person but the modern image doesn't much resemble Saint Nicholas of actual history. Modern commercialization has had a huge impact on Christmas and pushed gift giving over more traditional spiritual celebrations and, iirc, modern commerce invented Rudolph the red nosed reindeer (though I think it was a different company, not coke).

Google it yourself. You probably are in a better position to verify it than I am, with my wonky android browser freezing up and saying "bite me, bitch" on a regular basis.