Antioxidents don't prevent rancidity, and I'm not sure that olive oil is any great antioxident powerhouse in any case. Swallowing a small cap of rancid oil isn't the best either, but it often happens with oils like fish oil caps etc.
The idea of swishing around a rancid oil in your mouth for 20 minutes is not very appealing. Will it injure you? Likely not but yechh!