Yes, insofar that they think they are committing suicide. In the end the whole thing is a ruse concocted by the other doctors. It’s intended to be comedic in execution.
A baby is brought into a military hospital in Tokyo for a severe illness, but he is only on screen for a short time and is not mentioned throughout the rest of the film
A young soldier is hit in the throat and spits up blood while on the operating table, and there is a small amount of blood during the football match running down the cheeks of one of the players, but no vomit is shown in the film.
There is a scene where the dentist, believing himself to be a homosexual, tells Hawkeye he will commit suicide. A send-off ritual is performed mimicking the last supper, ending with him taking a "black capsule" but he does not die.