Do pet parrots stuff things in their crops for later?

Most birds have crops. Whether the bird is wild or domestic, the crop functions in the same way - to store food.

"As mentioned in a previous article, the crop has one function - food storage. Without it birds would have to eat constantly because of their high metabolism. The crop is involved in moving food into the digestive tract. One of the signs that the crop is actively working is that the muscles can be seen contracting as they push the food stored in the crop into the stomach."

http://birdsnways.com/wisdom/ww63e.htm

"Crop: In the same way that a chipmunk stores food in it's cheeks, birds store food in their crops. The crop is composed of layers of muscle tissue, and holds and softens the food until it's ready to be passed on to the gizzard."

http://birds.about.com/od/birdhealth/a/birdanatomy...

"Not present in all birds, the crop serves more or less as a "doggy bag" when the bird eats. Notice the crop in the picture above. Let's say you're a Song Sparrow and you discover a weed just loaded with delicious-looking seeds, but the weed grows in the open. If you flit into the open area to eat the weed's seeds, you're making yourself vulnerable to predators who want to eat you. What to do?

What you do is to flit into the open and gobble up those seeds far faster than any stomach could possibly handle them, then fly to safety. You can do this because of your crop. For, as you cram in those seeds, a few at first go straight to the gut but, when that fills, further seeds begin detouring to the bag-like crop. Once the crop is full of seed, you fly to your favorite perch, and now there's not much to do but let your stomach digest. As those first seeds in the stomach begin working their way through the rest of the body, seeds stored in the crop automatically refill the stomach. If someday you pick up a bird, perhaps one that has flown into a window and you want to save it from the cat, if that bird has recently eaten, you well may be able to feel the crop in the chest area, feeling like a bag filled with grit right below the feathers.

Actually, specialists in the field of bird guts would want to insist that some birds have real crops, other birds have "pseudocrops," and that there are other croplike variations, but we don't want to get too confused so we'll just leave it at that."

http://www.backyardnature.net/birdguts.htm

All the food a bird eats is stored in the crop for a period of time. The only way it comes back out of the crop through the beak is if the bird regurgitates. They don't purposely store food in there to eat later. They may regurgitate it later for offspring or for a mate (which can include a human they are bonded to). Birds' metabolism is very fast so it doesn't (and shouldn't) stay in the crop too long.

Hope this helps.

Hilarious.

No, birds are not like rodents. They don't use their crops as cheek pouches.