No, your wife cannot claim the standard deduction if you file as Head of Household and itemize. Under IRS rules, if you are still legally married, your wife’s standard deduction is reduced to zero the moment you choose to itemize on your separate return. This means she will be forced to itemize her own deductions as well, even if she has no expenses to list and ends up with a deduction of $0.
While you are technically "considered unmarried" for the purpose of choosing your filing status of HOH, you are still legally married for the itemization rules.
