The game, and show, clearly intend for the player/viewer to take away that a vaccine was absolutely possible with Ellies body. It isnt left vague at all. Trying to dig into the real world science of it is just silly. Many works of fiction require a certain level of suspension to buy in, we are talking about a zombie apocalypse here.
In subreddit r/shittymoviedetails
In a post titled:
In The Last of Us they want to kill Ellie to develop a cure for the zombie infection, whether the cure would have worked or not is purposefully left ambiguous to show that Joel had already made his choice and- oh nevermind Neil Druckmann confirmed that it would have worked in an interview.