What we talk about when discussing effects of bleach is the long term (repeated) exposure of cotton to chlorine bleach in laundering.
The one time bleaching of the fabric prior to manufacture, while not ecologically very nice for the local watershed from what I'm told, will not significantly alter the cotton other than its color. So your only consideration is aesthetic.
However, using chlorine bleach repeatedly over the life of a gi will weaken the fibers (it is possible to soak thin cotton, like than in underwear, in strong bleach solution until holes develop--I've done this). Best option is a non-chlorine bleach.