I always wondered what might happen if he had an appendicitis.
Well, I'm no doctor either, but I bet it would have been very very serious. On the one hand, you can't risk the appendix rupturing, because that would cause peritonitis, which often results in death. (Especially in those days before antibiotics--my own father, at the age of 5 in 1927, very nearly died of a ruptured appendix followed by peritonitis--and he at least wasn't a hemophiliac!) On the other hand, if you do surgery to remove the appendix, that necessarily involves bleeding, probably a lot of it. External bleeding could generally be controlled by applying pressure, but I don't see that being effective in major surgery--which after all is what an appendectomy is!!
I really can't imagine Alexei, in the days before blood transfusions and antibiotics, having a chance of surviving major surgery. I would think he would have bled to death.
After all, a simple nosebleed once came very close to killing him!