It is possible. You should be testing yourself with a home glucometer to see how low and how often you get low and how long it lasts. Low blood sugar starves cells.

You can help control low sugars, by eating smaller more frequent meals....and for snacks use nuts. That is what I do.

You can test yourself every 2 hours for a day, every once in a while to see what is going on. Your normal A1C points to average postprandial (after meals) levels with no alarming spikes.
But the A1C can also be showing that your blood sugars are not high enough at times for your cells.

Alot of lows happen when you are sleeping. I have found a connection between having arms falling asleep at night and having lows. I keep Zone bars next to the bed and if I wake famished I have 1/2 of one. I just found a new Nature Valley snack bar this past week at WalMart. It has protein in it like the Zone bars and is same calories without the vitamins added and 1/2 the price. They are a little bitter (some dark chocolate)...but they work. I prefer the fruity Zone bars for night snacks...not the chocolate ones.

Reactive hypoglycemia means the insulin levels get too aggressive after eating and your blood sugar comes down too fast. So eating carefully controls that.
I had this for many years (almost 20), before I finally started with elevated morning sugars fasting.