The simple fact is that many people don’t eat surrounding their workouts. They think it will undermine it or otherwise not work with it. One reader specifically wrote in asking about this recently, and it’s a common misconception, it happens. Her problem was that in all actuality she would go for an hour in the mornings and hit a crash of energy after. It was also mentioned that her class is at 6 in the morning. I will be the first to say kudos to you. I’ve never personally had the discipline for it.
But that being said, it is not against the rules to eat around your workout. Whether you eat before or after depends on you, but your body needs that energy to function in general terms and you are burning off a number of calories. It’s unhealthy not to replenish those to some degree, though of course you want to burn more than you’re taking in. The reality is that you have to take care of yourself. So no, it’s not going to hurt you to eat around it, in fact it may even help you, especially in avoiding those crashes. I would definitely recommend it.