Are you wanting to continue using Armory... or are you just wanting to recover your private keys and migrate to another wallet? 
If you want to continue using Armory, then yes, you'll need to wait for Bitcoin Core to finish syncing.
If you just want to recover your private keys, then you can find my guide here on how to export your private keys: https://bitcointalk.org/index.php?topic=4746784.msg43255691#msg43255691
Note: you will need to use the "Include Unused (Address Pool)" option (and get about 1000 keys) as Armory has no way of identifying the "used" keys until it has been fully synced (which it obviously can't do until Bitcoin Core is fully synced
)...
Once you have all your private keys, you can easily import them into another wallet like Electrum.
It really comes down to what your plans are moving forward, and whether you are in a "hurry" to access your coins etc.
If you want to continue using Armory, then yes, you'll need to wait for Bitcoin Core to finish syncing.
If you just want to recover your private keys, then you can find my guide here on how to export your private keys: https://bitcointalk.org/index.php?topic=4746784.msg43255691#msg43255691
Note: you will need to use the "Include Unused (Address Pool)" option (and get about 1000 keys) as Armory has no way of identifying the "used" keys until it has been fully synced (which it obviously can't do until Bitcoin Core is fully synced
)...Once you have all your private keys, you can easily import them into another wallet like Electrum.
It really comes down to what your plans are moving forward, and whether you are in a "hurry" to access your coins etc.