Considering the process was fairly convoluted, and because I entered on a multiple entry tourist visa I opted to travel within that range, and just bite the fine on the other end. Similar cost money wise. While I had originally intended to go the permit route, the earliest appointment available was April 22. This would mean that I would not have access to my passport during my spring break travels. Not ok.
I would recommend getting the permit if possible. And if you are staying the full year, especially. But try to book your appointment before you leave for Turkey.
*your health insurance must be notarized & translated. International Student Affairs Office will not tell you this. I used my friend’s turkish roommate. You can reach her at email@example.com if she is still in the area. I wouldn’t panic though, as with every other process they are not too picky. They just want to see the the gov is not financially liable for you in the event of any emergency.