Maybe, but you might also find that you end up on Microsoft's Xbox Live ban list if you do something like that. No one except Microsoft really knows the full extent of what they can monitor about your console via Xbox Live, but I wouldn't think it too difficult to figure out you have a US sold system with a drive sold in Japan. Whether or not they decide that's worthy of banning is purely at their discretion.

Keep that in mind and weigh the risks against the benefits before ordering.