Yes if you move the german AA to italy, it still preserves the German Tech advantage. I played a multiplayer game where Japan got radar and shot an AA through the suez to help protect in europe.
You can also move multiple AA’s around for rockets, however, keep in mind that each territory can only shoot one IC (regardless of how many AA’s are there) and each IC may only be hit by one AA/rocket during a turn. If germany has 10 AAs, but those rockets can only reach 4 ICs, it can only fire 4 rockets.
Also keep in mind that since the Rocket fire is part of combat, you can’t fire it and non-combat move the AA on the same turn. You have to move it into position first, then fire the next turn.