As Iztok alluded, there have been threads on this subject before. I checked out a few when I noobed in.
IIRC, one or two folk set up some tests using corners of a gigantic map, well beyond any possible AI sensor range. In some cases, the corner had a juicy planet. The player poised a colony ship there and waited, with a screen of sensor-mounting ships or bases or something to see what happened.
With no previous scouting, colony ships soon made their way directly at the juicy planet.
Re-running it with the planet colonized, the AI colony ships never showed.
Re-re-running it, I believe the AI ships diverted as soon as the planet was colonized.
So, the AI seeing the map for planets was pretty much proven.
I do not recall a similar test for resource points. However, I have seen AI behavior so similar to that described in the above tests, that I have concluded that the AI must "see" the resources just as they do planets.
There is a major delta, though. I have seen destroyed resources quickly claimed by AIs not the original holder and not the attacker, but I have also seen the same resources left unclaimed for practically forever. The hypothesis I have made is that when the AI "turns off" the Colony Rush thinking and stops making colony ships and converts those left or whatever, that this same decision point must "turn off" the knowledge of the status of resource points, at least those beyond their sensor reach (and maybe all).
You see, in other 4X space games, there is a "scorched earth" option, where one wipes out a colony planet, sterilizes it, and the planet must then be recolonized all over again. This means that the AI elements that colonize must remain active all game. This is not the case in GC2. Once all the planets are colonized, the AI can and must abort the routines that it uses for the Colony Rush. So, I think the resource grabbing routines are elements within the larger Colony Rush rouotines. Thus, once the AI stops using the Colony Rush modules, gone also is the distant resource grabbing elements.
Maybe I'm wrong, but it seems to fit the AI behavior as I have observed it.