I agree that the AI will ignore doings within your borders, including military buildups. Also, the AI will react especially ineffectively during the initial invasion. In fact, it reminds me Stalin's behavior during June-August 1941. Papa Joe (per some biographers) closeted himself for three days after the start of Barbarossa and would not speak to anyone or give orders. In the days ahead of June 22, 1941, Soviet commanders had been refused permission to patrol their own side of the border, were told not to react to provocations (some even were orderd into barracks and their weapons stored), and the fleet admiral was refused permission to up-anchor and stand out to open waters. Incidentally, most of those same Soviet border commanders were later executed for failing to do the things they asked to do but were told not to do. Stalin and his henchmen wanted to cover their tracks. The only notable exception survivor was that Soviet admiral, who had insisted on getting those orders in writing.
I have played games where the AI shifted a force from destination to destination, or target to target, without ever getting to use those units on anything in any sort of timely fashion. That, too, has happened historically, and even did so a few times on the German side of Barbarossa, mostly due to Hitler's interference.
The choice of Barbarossa as a source of examples is not w/o basis. That conflict is the probably the closest thing we've had on this planet to a GC2 invasion. Consider: huge borders, great distances, vast forces, lots of machinery needing ammo and fuel, fast communication yet limited intelligence, both sides under the command of a single decision-maker.
Also, I agree that the AI will often not react to visible enemy units, and stupidly continue on in conformance to its original orders.
One of the D-Day anecdotes involves a line soldiers tramping along one side of a wall and another line of soldiers tramping along the other side in the opposite direction. At one point, the wall was lower, so that they could see each other. The two units marched by on their separate ways and only too late did one or both realize that the other was an enemy unit. When some turned around, the other was already out of sight.
At Jutland - arguably the greatest sea battle since the advent of steam, during the night after the vast but inconclusive battle (May 31 - June 1, 1916), the British admiral (Jellicoe) tried to put the Grand Fleet across the expected path of the German fleet to port. The German admiral (Scheeer) chose a somewhat different course, but the German fleet still passed through the British line. Many, many British sailors and officers and even ship captains and maybe even junior admirals saw the Germans but no one reported it. They all figured that if they could see them, the admiral in charge must and they would do nothing without orders. A few separated British ships actually fought the Germans during the night because the Germans essentially (and in one case literally) ran them down. Yet the British admiral never was told and the Germans got through the line and back to port.
If humans suffer these things for real, imagine trying to code the poor AI to do much better!