To make a pleasant change for everyone I'm not saying much at all.

What I've done is to report what some studies have found. It was the crop size thing that got me going because I know a bit about crop size limitations when it comes to feeding. I read at least three times the number of studies around the topics in my research. What I didn't know and this is the part I'm really interested in was that according to the studies a chicken can divert food to the crop or the proventriculus.
This is what's interesting. The studies say that it is the amount of food held in a chickens crop that makes it eat. Full crop = no more room so don't eat. Empty crop = eat. Seems reasonable.
Some of the studies state that what determines where the chicken sends the food is largely determined by how it is fed. Food constantly available, chicken sends food directly to the proventriculus and bypasses the crop. No need to store if there is no shortage of food.
Seems reasonable as well.
If a chicken is fed on a meal time basis (a quantity of feed given until eaten or removed after a period of time) then food is directed to the crop. We can see this when chickens try to fill their crop before roosting. They know there is not going to be food available during the time they roost. This can be anything between 14 hours and 6 hours roughly.
So, we have the two extremes but many of our chickens don't get fed at either extreme and nothing I've read deals with this and nothing I've read explains the exact mechanism by which a chicken diverts food from place to another.
So, I can't answer your question. If it's a conscious choice then the chickens takes one more step up the smarts ladder and it's a big step.
It can't really be done during a necropsy. Firstly one would need a dead chicken with a crop full to capacity. Lots of changes happen to the body shortly after death.
With a set of calipers to start with. Later I filled a balloon with a quantity of feed (dry crumble) and felt a crop and then the balloon; adding or subtracting until the balloon and the crop felt the same. It's not exact but it's surprisngly close.
The addition of water primarily although I believe some commercial feeds have additives that make the chicken eat more.