Just read an MTV interview with Melissa Ponzio, in which she confirms that Noah was killed by The Governor. She also mentions that he was likely not Karen's son.
Interview contains spoilers!
Here's a snippet:
"MTV News:What happened to Noah? Can we assume that he didn't survive Woodbury and the governor?
Ponzio: Yeah. Noah got it. Noah is commonly referred to as "asthma boy" and a lot of people thought that asthma boy was my son. But Laurie Holden and I had this whole backstory that he wasn't my son, it was more that maybe Karen had been a schoolteacher close to Woodbury. So I knew a lot of the kids and that Noah was one of my students. When he was pulled to be one of the governor's raunchy army guys I was sticking up for him because I knew that the governor was marching him straight into death. And he did. And he's dead. I know, it's harsh."
I apologize if this has already been posted.