Failure to properly chew food (especially meat) can cause a medical condition known as Steakhouse Syndrome where a bolus sticks in the esophagus.
Whilst this can sometimes resolve itself naturally, in extreme cases surgery is required to dislodge the offending lump of food.
Having had to experience such surgery myself, I certainly wouldn't recommend consuming larger and larger chunks of food as a matter of course.
As for what actually happens if you do consume large chunks of food - they do take longer to digest as they're not completely broken down in the stomach but are passed through in partially undigested form to the intestines.
On the back of this, you may think this would make you feel fuller sooner but actually, the opposite it true. It is signals from the stomach that indicate to your body that you're becoming full. During World War II when food was scarce, the government recommended eating slowly for exactly this reason - that you would give your stomach sufficient time to let you know you were full so precious food would not be wasted.