Yes, due to voucher it will get posted to account. They want the SSN should it get separated from the voucher, as they get millions of pieces of mail.
The do research on misapplied checks so you should be Ok anyway.
The reason for U. S. Treasury is to help prevent theft of checks going to IRS. People have been known to type over IRS and change it to MRS. ABC, and cash it. But it appears you spelled out Internal Revenue Service.