I assume you are talking about using the current partnership payroll system to pay the nanny so you don't need to get a personal EIN and file the quarterlies separately... can you do this ... yes you could HOWEVER you must keep excellent records for the 1065. It is not an expense for the partnership and NO PART OF IT cannot be deducted as expenses on the 1065 ... instead it must be listed as part of the partner's guaranteed payments.
This situation may be a focus of an audit so it is not the most correct way to handle it ... it would be better to keep it totally separate ... get a personal EIN to pay the quarterlies and issue the W-2. They are free and easy to get ... https://www.irs.gov/businesses/small-businesses-self-employed/how-to-apply-for-an-ein
