Well, no. The taste differential between milk labeled organic and the regular stuff is caused by the fact that they are processed differently. Organic milk, just like aseptic milk has been subjected to ultrahigh temperature processing. This lowers the vitamin content of the milk and destroys some of the proteins but it caramelizes the sugars which makes the milk taste sweeter.
If you like the sweeter taste then you would be better off buying the aseptic milk which tastes the same but is cheaper and has a much longer shelf life.