If it would cause no harm to deer, I would say yes, but it would feel strange hunting in the spring (would be harder as well).
The seasons are as they are for a reason (one being to foster fawn survival). For example, in our specific area of the state sometimes fawns drop late, so in only our area the first 2 weeks of archery are buck only. This screws up my odds of getting an easy kill (harvest), but maybe it does some good.
I know what my wife's opinion on this subject would be.