Ultimately, there are only 2 outcomes.
Your Federal case continues to be denied until you can no longer appeal it but you continue to receive benefits on the the new claim.
Your Federal case is approved and SSA pays the backpay you are due. Since you are already receiving benefits now, you will not receive benefits twice for any months you were already paid - but you may receive a small amount for the months you previously received payments- if the new onset date results in a higher benefit amount.