Alaric's much less valuable to either empire with Theodosius still ruling a united empire. His main use was essentially for each side to play him against the other and use him for their own devices. Though I have my doubts Theodosius could defeat Alaric-if he could defeat the Goths, he would have, rather than signed a treaty with them.
As for the migrations-well having stability on the throne, especially with a strong willed ruler like Theodosius, will do wonders for the empire during that period-it wasn't the migrations really, but the instability that followed Theodosius' death due to him having two easily controlled young heirs, that was the real problem the west and east faced. More importantly, Theodosius' sons will have grown into adulthood by then. Maybe Honorius won't be a total fuck up, and Arcadius might grow into a decent ruler.