If The Governor has an army with him then Michonne and her katana won't do much good.
I agree that sometimes situations are out of your control and that against an army, her katana wouldn't go far. But I don't see her surrendering and being captured. She might lose the battle, but she won't get taken alive. Just my opinion.
Michonne was on to the Guv from the beginning. She knew he would send his henchmen after her when she left Woodbury and he did.
That wasn't really my point though. I do agree that she would do everything in her power to prevent herself and Hershel from being taken hostage, but sometimes things happen beyond our control. I think that they showed her stumbling with her horse earlier this season to show that she is human and not an unbelievable, invincible cartoon hero (like it seemed last year when she was climbing trees without branches and jumping from unrealistic heights).