Out of F-1 status for one month!?

You will have no problems leaving. Make sure you hand in your I-94 or they will think you have overstayed longer than you already have and be barred from reentry longer. With an overstay of more than a month, you will be barred from reentry. As a practical matter, once you have been barred due to overstaying, it is more difficult, often impossible, to get another visa even after the term of your bar is completed. Also, since you are "in the 'puter" and other countries share info, you could very well have difficulties getting visas for many other countries. Plan on staying home.