Several source suggest they don’t.
With few exceptions, we learned that Medicare Advantage plans pay provider rates at or close to fee-for-service Medicare rates. Similarly, Medicaid managed care plan payments are close to the relatively low Medicaid fee-for-service rates.
[T]he rates paid for Medicare Advantage enrollees are similar to or slightly above those that Medicare pays for FFS patients’ care.
MA plan hospital prices are not tied to prices in the non-Medicare market, which is consistent with what we have heard from plans and other market participants. Non-Medicare physician payment rates also appear to have at most a modest relationship to MA bids, suggesting that physician payment rates may be partly anchored to FFS prices.