To truly have no sense of taste you would have to be both anosmic and aguesic as taste is only sweet, salt, bitter and sour. All other "flavours" are actually scents.
Incidentally that is why fancy wine testers "chew" the wine. When you drink the soft palate automatically closes off the passage to your nose. When you chew it relaxes and allows the fumes to carry the "flavour" to to the nose.