As far as the state rules in force go, yes. Virginia’s home care organization regulation, 12VAC5-381, does not say where your office must be. Neither it nor the licensing statute says whether the office can be in a home, and neither mentions zoning. It does require you to comply with "Other applicable federal, state or local laws and regulations;" 12VAC5-381-150 B 2, so local zoning decides whether a home office is allowed at your address.
Wherever the office is, you need regular posted business hours and to be fully operational during them, the license posted for public inspection, records kept confidential and safe, and someone able to receive an unannounced OLC inspection.
Worth knowing: a 2022 draft rewrite would have required offices, branch offices and drop sites to be in buildings zoned for business or commercial use. That proposed stage was withdrawn on April 7, 2022 and is not in force. A later version has not been published.