Nope.

Read No.3 carefully:

(ZT)

Special Rule for Separated Parents

 

Married taxpayers who are separated or estranged from their spouse may be able to file as Head of Household, even though they are not legally separated or divorced. Taxpayers who meet all five criteria below may file as HOH instead of the less favorable married filing separately status.

1. You file a separate return.
2. You paid more than half the cost of keeping up your home for the tax year.
3. Your spouse did not live in your home during the last 6 months of the tax year. Your spouse is considered to live in your home even if he or she is temporarily absent due to special circumstances.
4. Your home was the main home of your child, stepchild, or eligible foster child for more than half the year.
5. You must be able to claim an exemption for the child. However, you meet this test if you cannot claim the exemption only because the noncustodial parent can claim the child using the rules for children of divorced or separated parents.