Clearly his strength would be the only thing in question... Hamilton has trained to be a speedster. If he wished to sacrifice a bit of speed to gain strength, I don't doubt he could.
Speed comes from having an abundance of fast-twitch muscle fibers, great body control, good balance, and flexibility.
Bat speed can mask natural strength/power. I too believe that Hamilton could train/generate a strong swing by using speed to the ball. I'd rather him not sacrifice contact/patience/running speed to do so though.
If Hamilton did not possess above "mere mortal" athletic abilities, he could not have been trained to become an above average switch hitter in 2 years. Clearly he is WAY more bio-mechanically in tune than most merely "strong" athletes, which allows him to adapt and overcome much quicker than those type of athletes. Additionally, his arm strength is somewhat nullified by his range and ability to get to balls that others can't.
He has an ability that is outside the realm of definitive baseball theory. His ability as an athlete are why those theory's aren't law. Feel free to step outside of the old-school principles that are still ever adapting with this outlier of a case study.