I'd argue interval training is more valuable than absolute pitch in improvisation. It's rare you find yourself in a scenario where key is unknown and unknowable, especially playing with other musicians. Being able to hear and distinguish a minor 3rd from major 3rd is much more valuable.
Additionally, it's the intervals that give music its emotional content. For example, a minor third sounds "sad" while a major third sounds "happy". Absolute pitches are meaningless in this regard.
Playing a single note confers no meaning. It's only when subsequent notes are played that a context emerges, and music gains its emotional qualities.
