It could help you make personal progress by exposing you to a new problem space, and that may help you transition to that problem space full-time, but a 20% project itself is very unlikely to help you get promoted, and getting promoted is the most concrete way of evaluating of career progress, and a big part of most people's career goals.

For that, you have to knock it out of the park in your main job, not a 20% project.

Depends on your original role and what you do for 20% time. Some people setup volunteer groups, makers spaces, etc. that might not really fit their ladder so it makes it harder to grow. However, you can definitely take on projects that do align with your career path and can help with things like promotion. I've done 20% work helping to develop material for Coursera programs that did fit my ladder pretty well.