No. If you meet the qualifications for the home office deduction, you can take that deduction in addition to the $10,000 deduction for state and local taxes.
The home office deduction is no longer allowed if you are a W-2 employee. You may only claim this on your current return as an expense for your self-employed business. The home office deduction would not be included as part of your personal deduction for state and local property tax.