The rule is that you can claim the standard deduction only if your spouse does not itemize either.  So she has no choice, she must itemize.

And IRS doesn't send back MFS returns with no SSN for the spouse.  It's all a part of the Great American Tax Myth, that the federal government knows everyone's marital status and partner.  They don't even know whether Social Security recipients are still alive, according to the African-American in charge of cutting the budget.