Most birds have crops-- in fact, I think only penguins, gulls and owls do not (although there may be more I've forgotten). They may not be visible or palpable, but they are still there - large or not. In ducks and geese, they are quite small; just a little holding chamber, so to speak, on the way to the stomach.
A sour crop does not indicate a sour flavor, so sour vinegar would not effect this, anyway. Sour crop, which is usually known as a step up from "slow crop", describes a crop that is not emptying. The "sourness" comes from the fact that, in a crop that won't empty, there is often spoiled food... Bacterial and fungus infections, then, can become serious issues. And ACV is quite different from regular vinegar, particularly the organic kind that has been mentioned. I don't care what anyone says; I have been using ACV for years in many different bird species - ducks, geese, chickens; parrots, pigeons, doves... It is known to help move the digestive system along and many a time, along with a regimen of rehydration, has saved birds' lives.
Why is this? From what I have heard (although it is contrary to what one person just posted, I realize) ACV stimulates the digestive tract to move food along, similar to what apple sauce has been known to do. Unlike apple sauce, it does not leech fluids from the intestines, so is better to use when dehydration is present. It also kills bacteria and fungus quite well. It is often used as a disinfectant in the parrot world; one of the only things that will effectively kill Aspergillus fungus, for instance. I have used it before as a disinfectant when handling that very thing. It is also good to note that, apparently, organic, unpasteurized ACV "with mother" has a decent quantity of natural prebiotics and probiotics. I'm not sure whether or not this is just all talk, but one thing's for sure: ACV does have a use.
Of course, ACV cannot replace real medications. It can help, it can provide supportive care, but it will not help with heavy infections. Many vets suggest using ACV when a fungal/bacterial infection is present, but is too slight to warrant antibiotic/antifungal use. In short, it is a good supplement that, while having very little use in terms of nutrient composition... Is largely effective when used for low-grade, chronic fungal and bacterial infections, or just getting a bird back onto its feet. Really helps to use it when they are under stress, along with vitamin water and hydrating fluids.
I also thought it important to note that, although ACV is vinegar, and you'd think it is highly acidic... It is not. It is quite the opposite. It is said to be "alkaline". That is probably why it would neutralize stomach acids.