Thanks for your question! For characters in that situation, it's honestly up to you whether or not you want him to know. The medical staff may not immediately volunteer that information, but it might slip out or the character may overhear it if they wouldn't ask, and they would absolutely tell the character the truth if they were to ask directly.

Essentially, the answer is that it's up to you and what would be the most fun for how you want to play your character!