Key points are not available for this paper at this time.
Somesh Das Gupta, Michael D. Perlman, Power of the Noncentral F-Test: Effect of Additional Variates on Hotelling's T2-Test, Journal of the American Statistical Association, Vol. 69, No. 345 (Mar., 1974), pp. 174-180
Gupta et al. (Fri,) studied this question.