Will the order in which you hook up the light bulbs in series affect the intensity of light each emits?

No... the order won't matter. Since the bulbs are hooked up in series, the total resistance across the circuit, regardless of the order, will remain the same. Therefore, the lights will have the same intensity regardless of the order.

Also, by Kirchoff's Current Law, the signed sum of the currents entering a node is equal to zero. As a consequence, in a series circuit, the current at every point in that circuit is the same.