Factually, yes. Drinking that much vodka in that short period of time could possibly cause death.
You would need to calculate your Blood Alcohol Concentration (google it). Once your BAC reaches .30% and higher you are into the coma and death stage. BAC is based upon Quantity over Time and depends upon your Body Weight. For example, someone who weighs 100 lbs would only need to consume 8 drinks within an hour to reach a BAC of .30%. But if someone weighed 200 lbs drank the same 8 drinks in 1 hour they would only have a BAC of 0.15%. In your example a 26er is slightly more than 750ml which translates into 15 standard 50ml drinks. So if you were able to consume a 26er in 10 minutes you would likely die unless you had a very large weight.
But realistically, no. Before you would be able to consume the required quantity you would likely pass out. And thus fail.
Especially as someone who doesn't normally drink. You would likely get sick, vomit, and pass out way before finishing the bottle. Many times when you hear of people dying of alcohol poisoning it is usually in a situation like a hazing ritual. But the person is likely too drunk to continue drinking by themselves and so someone is "helping" the person drink more alcohol.