No. You cannot use a disabled person who is not related as a qualifying person for head of household.
You might be able to claim the person as a qualifying relative dependent and get the $500 credit for other dependents, but since they are not related to you, they cannot be your qualifying dependent for Head of Household filing status. There is a big difference in who can help you qualify for HOH filing status.
Qualifying relative
When you add someone as a dependent, we'll ask a series of questions to make sure you can claim them. There may be other tax benefits you can get when you claim a dependent.
Related Information:
What is a "qualifying person" for Head of Household?