Normally I would say yes, you can write it that way, and it doesn't mean anything different, nor does it infer any part of it is more essential than another.
- Around the world, Grammarly helps millions of users.
- Grammarly helps millions of users around the world.
These two examples mean the same.
However, your example includes technical detail - it speaks about users and platforms - so you need to make sure it makes technical sense as well as grammatical sense. Who or what is spread across "platforms" - Grammarly, or the users? If the users are across platforms, then it should be left as it is. Your edit suggests that Grammarly is operating across platforms, which some might argue is not possible - the same product might be coded multiple different ways to work on different platforms, but the software itself does not cross over from one to another. Just a thought.
Also people tend to remember what was said last - so it depends whether you want the 20 million users or the multiple platforms to stick in people's minds.