it doesn't. I have done it both ways on the same rifle to see what would happen.
A grand total of nothing changed.
If the recoil lug and areas around the action screws are properly done, the action is fully supported. Whether you bed the tang or not is entirely up to you. Same goes for around the mag well.
Personally, I prefer to bed it as I don't like seeing that gap everytime I am behind the trigger.
In most stocks, the tang area is about 1/4" square. If you think this amount of area can affect your action harmonics, better start weighing them primers...
Jerry