Even if you win the lottery abroad, can you bring it all in cash upon returning?

The scenario is: you've managed to receive ₩500,000,000 (~$337,265) at a Korean lottery (the catch is, only given in cash) which is delivered to you in two duffel bags. However will there be issues when returning back to the USA with that amount of money since it's bundles of cash via foreign currency when the cap is $10,000 for undeclared amounts?