Hi Nino
In short: Yes, it is possible. However, you will need to understand basic Joomla ACL in order to setup the system like that. By the way, the upload files is handled via Joomla Group, not for individual user. So if you want it work for individual user, maybe for each user, you will have to create a Joomla group for him.
Hope my answer is clear to you.
Tuan