I know that you haven't seen Mugen in a minute...but he is fucking GINORMOUS. He's SO fat that he doesn't even sleep on his belly like a normal rat, he's so big he sleeps on his side, and he sleeps so damn soundly that I ALWAYS think he's dead when I walk in the room . The other one we adopted in January was so fat when we got him that we playfully named him "Lardo" . The third one, Yang, however is still very thin and fit. How big the rat gets usually depends on how active they are and how much they naturally are inclined to eat, and it varies widely in rats, hence why my boys are huge and Ying is fit.
But...can they eat until they die? No, they won't. If they eat and eat and eat (and I know it seems like it's an UNGODLY amount) they will basically fall asleep, in my experience, and sleep it off for awhile. People think I'm horrible but I definately spoil mine with treats because they get so damn happy when I give them some, and we're talking about animals that only live 2-3 years so long term effects of being a bit overweight don't take as big of a long term health toll as with humans, so I wouldn't worry about them eating too much .
Also, if you notice your rat taking a LOT of food when you hand it to them and they keep coming back for more without stopping for a good nap - 90% percent chance they're taking it and hiding it somewhere. Hoarding is definately their nature, only someone that owns a rat will truely know the meaning behind the phrase "pack rat".