I do not think that Julian`s failed Persian campaign of 363AD and Jovian`s peace treaty did have so much importance for the Battle of Adrianople.
Thanks to Jovian the Roman field armies survived instead of getting annihilated in enemy territory and the Eastern Empire inherited a more stable border situation with the Sassanians. Besides some minor conflicts that relative peace secured the Easterns survival for the upcoming difficult 5th century.
Imagine what would have happened if the Sassanians attacked the Eastern Empire with full forces.