No, not in any meaningful amount.
While Medicare will pay for limited stays in a skilled nursing facility (rehab), if you become so frail or sick that you need to move into an assisted living facility or nursing home, Medicare will not cover your custodial cost. Seven out of ten Americans will need this type of care at some point in the lives.
Long-term care can exceed $100,000 per year for a private room depending on where you live. Long-Term Care insurance and Short-Term Care insurance both help to cover these cost, as can certain riders on life insurance policies and some annuities.
For this with limited income and savings, Medicaid can help fill the gaps.