Hi Kenneth,
it is not that simple to put 2 and 2 together.
After each submit the answers will be scrambled in time. That means you have to observe each submission and compare each submit content afterwards to find the user-submission relation.
So, if you miss the first user log you have no chance to put 2 and 2 together ;). You just know there is a submission but you don't know which submission is related to which user.
If that is not enough you could use the invitation plugin, to invite your users anonymously into your course.
Best regards
Andreas