'I'm starving! I'm going to go to Chick-fil-A and get stuffed', does it sound okay to a native's ear? British people would use it in a whole different sense but maybe a literal usage of that phrase would be fine with Americans, wouldn't it?
The idiom in English is: to stuff one's face.
I'm going to Chick-fil-A to stuff my face.
not: to get stuffed, which really would be comical, as it would mean to get screwed or to be stuffed as one stuffs a turkey.
I don't usually cite the Free Dictionary but it works fine here for a "reference":
slang To eat a lot of food, especially quickly and in a short period of time.
I'm a native English speaker from Canada, so my English is pretty close to American.
You could use it the way you want, but you would have to say "to get stuffed". You will be understood the way you intend and it won't sound weird.
You do have to be careful how you use it. It's true that we don't often use the phrase "get stuffed" the way the British do, but it is largely known that it is a British expression. So if I hear "get stuffed" I think of the way the British use it. So the context is key.