Kata is synergistic with everything else, by itself it can't do anything.

However, when it combines with all the other stuff you see benefit. The only 'power' training from solo kata is fine-tuning of certain body mechanics, it can definitely effect that, but it will not unless you 1) already have someone teaching you the correct body mechanics and 2) actually know how to use the variations in the kata against someone trying to hit you.

If you have that stuff, then solo practice works as an complimentary practive to the above things, and can give some definite improvement.