I just ran Bitcoin Core and it seems to be 4 weeks behind, though Armory didn't mention that.
It does not do that for you. Armory only cares about block data on disk to bootstrap its DB. It doesn't matter how far back in the past that data is.
Update to this at any rates:
https://github.com/goatpig/BitcoinArmory/releases/tag/v0.96.0.4