No, the lawnmower will not still run if gas is poured into the oil. Gasoline and oil are not compatible and mixing the two will damage the engine. Gasoline is a fuel and oil is a lubricant. When the two are mixed, the oil will become contaminated and will not be able to lubricate the engine properly. This can cause the engine to seize and fail.
If you accidentally pour gasoline into the oil, you should immediately drain the oil and refill it with fresh oil. You should also check the oil filter and replace it if it is contaminated with gasoline.
