I was on a plane that ingested a bird. No damage to the engine, and it was a smaller (BAE) commuter jet. What was wierd is that the cabin filled with a smell like chicken fried in motor oil. I guess the cabin pressurization pumps run off the engines and the intakes are close enough to pick up that smell.
At one time I did high-speed photography of engine tests at GE. During a bird-ingestion that engine will shake, rattle and roll.
In my short tenure at GE, I never saw an enging come apart as a result of a bird ingestion (but that don't mean they won't).
I can envision the engine on the AA plane bouncing and jerking after ingesting a bird or birds and coming off because of a structural problem with the pylon or wing.
Actually, quite easily. A large bird like a Canadian goose being sucked into an engine traveling at 300 MPH can and has caused catostrophic damage in the past. It is a major risk and one of the reasons that airports use measures to keep birds away from the runways.
This being the fall, a flock of geese or other migratory birds could well have crossed the path of that flight.