I don't think it would do that much damage to the brain if you deprive the brain of oxygen it wouldn't matter as much as the brain does not need as much as the rest of the body. Although might cause a embolism
Yes. You do not feed your brain oxygen while choking. While given no oxygen, brain cells die (it takes more than a minute though). Unlike skin cells, brain cells do not grow back. Be it on water, candy or someones hand, brain damage can occur after long enough.