The answer is not likely. It’s certain that Botox is a topic that has no relevance to the jaw, meaning the chin or mandible. There’s no effect on the mandible. The mandible tends to shrink due to atrophy. So as you get older, the mandible shrinks. Also, you tend to lose teeth and you lose other bone support. This shrinking of the mandible has been proven by CT scans.
We know that the facial skeleton changes with age, it tends to get smaller and the mandible tends to lose its mass. It is unlikely that this is caused by Botox; it is just a natural ageing process. Bone resorption in the lower jaw occurs naturally with age.