“as a noncombat move by land units of a power
that is at war”
since the AAA gun is a land unit, I don’t see why not. Nothing under AAA says that it is limited during the noncom.
Ok, if the Axis attacks and fails, the territory does indeed belong “to the Allies” and to a certain power you choose (Russia, UK etc.).
But, you cannot independently attack with those units, load them on transports, or get the income, until you have “liberated” the territory by placing a friendly allied land unit there.
Example;
Italy attacks Yugoslavia. All the Italian units retreat or die after the first round of combat. They get no casualties or hits. Place a face down UK marker and 5 UK infantry there.
Now, the twist is that you CAN land airplanes there (after it has been unsuccessfully attacked by the Axis), as just as the DEI territories, they always friendly. However, you cannot assert control with air units. So, you can never place markers, take income, etc until a land unit has visited that territory.
Only after “taking” the territory during noncoms can you flip the control marker, add the income, and begin controlling the infantry (next turn).
This will happen very rarely.
The exception is Mongolia. If Japan activates war by attacking a Russian held territory adjacent to Mongolian held territory, you place the control markers and the infantry. They are imm. under the control of Russia and can move or attack starting on its next turn. You can blitz through the empty (non Japanese held) zones on your turn; you don’t have to stop and control them.
In other cases, (through an untouched Persia to untouched or enemy marker northwest Persia), you cannot blitz because you cannot blitz during noncom and you must stop to “raise flags/place control marker” even if you had 1 move left.