Falafel themselves might or might not be vegan (I've seen recipes that contain eggs, and some that don't), but it would almost certainly be served with a yogurt-based sauce.
Can't speak for every kebab shop but here it's typically served with hummus, tahini and sometimes an eggplant spread.
Edit - also the traditional way to make falafel is vegan as it originated as a fasting food for Middle Eastern Christians (traditional fasting rules dictate no animal products).
Edit - also the traditional way to make falafel is vegan as it originated as a fasting food for Middle Eastern Christians (traditional fasting rules dictate no animal products).