There is a possibility it could hurt their ratings if they signed Cena.
It's kind of a complicated question. Their ratings would certainly jump if Cena signed because a lot of him younger fans would start watching TNA. Hell, I'd say every wrestling fan would watch his debut with the company. I wouldn't be surprised if they did a 4.0 with his first Impact. It would be historic. The real question is what would happen over the next month.
Safe to say most TNA fans don't like Cena. However, the ones that quite watching would easily be replaced by the new viewers he brought in. Having Cena would be a double edged sword:
-His WWE fans like him because he's a superhero. If TNA doesn't book him the way his younger fans are used to, they could lose interest and stop watching.
-If they did book him as Super Cena to keep his fans happy, a lot of old TNA viewers would stop watching. They would probably not be fans of Cena squashing AJ, Angle, Joe, Roode, and anyone else they liked.
-They could try something to meet in the middle, but that wouldn't please the original TNA fans or the Cena fans they brought over when they signed him.
TNA could make some real money if they were able to do something with Cena that brought in all his WWE fans and made the TNA fans happy. Unfortunately, I think it would just fizzle out.