Short answer: No!
You're welcome to commit as much as you want. However, you only have one opportunity to push your solution. Once you've pushed it, the company will be notified and may begin reviewing your solution at any time.
But if you happen to push your solution accidentally, there's no need to worry! Simply ping the company and request a new invitation for a fresh start. This will enable you to add the new assessment's Git repository as a new remote to your local Git repo, allowing you to push everything once again.