The yeast is killed by cooking. In the case of fermented beverages most of the yeast settles out before you drink it and you do not drink much yeast. Your stomach acid kills what you do drink.

If you straight up drank active yeast slurry and sugar water it probably could overwhelm your stomach acid and ferment in your stomach and intestines, producing a lot of gas (co2) and some alcohol, but probably not enough alcohol for you to notice any effects in the time it would be in your stomach/intestines. It would likely be very uncomfortable.