Ah, my explain not good~
Yes, you can plane to knife edge no problem, but it seems getting thinner than that you have chance of splitting. More round bamboo is more likely to split, but it is not 100% will happen.....
Ive had times I able to plane it almost see through
Keeping the knives very sharp always helps....
I put down hard rubber strip under the bamboo, this helps mold to shape of bamboo and acts as if its flat surface.