I can't see how the rebels could succeed being outnumbered 4:1.
But if they were to somehow win, a few things could happen:
Amakusa Shirō founds an Amakusa Shogunate, a Christian state. I wonder if he would kill the emperor, seeing as said ruler's claim to be a god incarnate (or something to that effect) does not mesh with Christianity.
Japan would not persecute Christians or close itself to the world, with interesting effects. I can't really speculate further...
It does seem to me that Shirō would not be as bad as people always make Hong Xiuquan out to be, and Christian rule would not devastate Japan. However, with Christians a minority, I wonder how long this would last without some renewed missionary efforts.