Glycated hemoglobin is a form of hemoglobin that is measured primarily to identify the three-month average plasma glucose concentration. The test is limited to a three-month average because the lifespan of a red blood cell is four months. Fasting before the blood is taken isn't going to change something that's looking at the last 3 months. So I'm going to say no, however . . . . . . . .
If they're going to do other blood tests like cholesterol and lipids or whatever, they may need a fasting test, best to ask them.