Yes, you can leave the country and go to Asia without first going to Mexico. There will be no exit immigration control, and since you're leaving, you're doing the "right thing" anyway. You might be banned from entering the US for either 3 or 10 years, depending on how long you've been there out of status.
*** El Cafe ***
N400 - NYC (Brooklyn)
March 12 2010: Sent
April 7 2010: FP done- walk-in
August 3 2010: ID decision not made
December 12 2010: Lawsuit filed under 8 USC 1447(b)
March 31 2011: 31 Oath date
April 1 2011: Passport applied, picked up!