not really. The average monthly stipend (that only 15% even get) is 579€, which is arguable not enough for rent in most bigger Cities (and that is ignoring that you also need to eat). The vast majority of students are either financed by their parents (the stipend is dependent on their income and if they earn more than a certain amount they a legally obligated to help their child) or by themselves. In Germany the university is mostly free (a couple hundred euros a semester), but most definitely don't live for "free".