No. When you apply for an ITIN via Form W7, you attach your tax return. So, your tax return is being filed by mail.
After the ITIN number is issued, the return is sent on for processing within the IRS. You DO NOT efile a return when its already going through the process. This will cause a duplication, which can cause a holdup.
If you did not include your state tax return, you can efile your state return only (i.e. do not click to efile the federal return) once you have the ITIN number.
