In the UK there have been effects, but it's too early to tell the full picture. Many drinks cut down their sugar content to avoid the tax and full-sugar drinks are often excluded from 'meal deals' (or the levy is explicity added, e.g. McDonalds' meals) so I would expect that people have be switching to diet versions in those cases. The Uk is pretty small so things can be changed at a whole country level more easily.
In the US? Maybe, jury is still out: https://text.npr.org/s.php?sId=696709717