A W-7 is not a tax return, it is an application for an ITIN. When we did our Form 1040 tax return last year, it did not take any extra time to receive the refund. Timeline was:
1/23/2023: Mailed package to IRS ITIN processing center in Austin Texas via USPS certified mail. Package included Form 1040 married filing jointly (With my SSN as primary, and her SSN/ITIN field blank), a statement that we are making an election under IRC 6013(g) to treat my wife as a resident alien for the purpose of our U.S. tax return, Form W-7 applying for ITIN, and her foreign passport (to prove foreign status).
1/27/2023: Package received and signed for by IRS Austin.
3/8/2023: Received Notice CP565, dated 3/3, assigning my wife an ITIN.
3/13/2023: Received Notice 14433 Return of Documents and her passport back.
4/6/2023: IRS transcripts showed our Form 1040 was posted. Refund was approved and scheduled to go out on 4/13.
4/15/2023: Received refund check in the mail.