The short answer is yes — but it depends on the insurer and will typically be more expensive. It's important to remember that "high-risk driver" isn't a definitive assessment. The level of risk can change over a person's lifetime.
Insurance companies consider drivers on a sliding scale of risk management, from very low (no-fault crashes, no record of speeding or risky behavior, etc.) to very high (multiple DUIs or speeding tickets, multiple at-fault crashes, etc.).