Yes, You pretty much summed up all T3 storylines, except for the "Learn to meditate with T3" optional sequence.
I guess he is almost as important as R2 for the era then. And no the rocket boosters are not necessary. And I have to admit that T3 is way better armed than R2. I mean, R2 have a electric taser/gun, while T3 have a nice gun, in addition to tasers/flamers/etc and self-repair armor.