No, it still wouldn't work and as it would be even worse than the first case as far as spoilage was concerned.
Assuming that we're talking about conventional, pasteurised milk, it should be remembered that pasteurisation is not all what it's made out to be. Although it kills many harmful bacteria such as those that cause tuberculosis, it doesn't kill all micro-organisms.
When milk goes off, there are a specific series of steps that happen as far as micro-organism growth and colonisation are concerned. First of all bacteria called streptococci convert a sugar called lactose to lactic acid. The acidity of the milk then rises. Then other bacteria called lactobacilli start growing at a tremendous rate and convert even more of the lactose to lactic acid. The acidity of the milk then rises even more. Under these conditions, mould, yeasts and other fungal organisms begin to grow and these organisms reduce the acidity. Then other bacilli start to multiply and these convert proteins in the milk to ammonia. The milk then becomes more alkaline and this combined with the destruction of enzymes leads to sour or decomposing milk.
So where do these bacteria come from? Well, they are present in the air, your fingers and hands, on pet hair that may be circulating in the room and suchlike. Pasteurisation of the milk may well have killed off many of the micro-organisms in the raw milk, but it cannot protect the milk afterwards. In addition, once milk reaches suitable temperatures, the micro-organisms that were not killed by pasteurisation begin to grow and multiply anyway. So milk can go off in an unopened, sealed container at room temperature.
So the type of stopper on the container is really immaterial. The only way to prevent micro-organism growth in a household environment is by reducing the ambient temperature to that of a fridge. Although bacteria, yeast and mould organisms are not all killed in milk at fridge