Unfortunately, no, Medicare does not currently cover non-medical custodial care, which is the bulk of adult day services. However, there are other methods that you can use to pay for adult day care.
Does your senior have long-term care insurance? If yes, adult day services are typically covered, though you would need to check with your provider.
Is your senior a veteran? The VA provides benefits for seniors that meet their requirements, and this includes adult day services. Additionally, Medicaid can indeed pay for adult day care services through what is called a Home and Community Based Services (HCBS) waiver.