No, I don't think it would. It would increase the supply of oil to the rest of the world, and decrease the supply to the US, which would depress prices in the rest of the world and raise them in the US, which in turn would encourage other oil suppliers - other than BP - to sell their oil to the US, rather than outside it.

The only way it would really harm BP would be if BP's share of oil production approached the US's proportion of global oil consumption, and even then, its effect would be to raise US oil prices.

For similar reasons, the notion of relieving the US from its dependence on foreign oil is similarly meaningless. Oil is fungible, and the price of oil for the man on a US street will still be affected by events in the Middle East, even if not a drop of oil he uses comes from outside his own country.

Maybe not a death penalty, but a pretty serious wound:

BPs total revenues in 2009 were $239 billion - of which about $130 billion was from the USA.

So if they stopped selling the oil in the US, there's no other country on earth that would have a use for it?

They would maybe take a % hit, however they'd still sell all their oil. Banning them in the US would not cause that $130 billion dollars to just "vanish"