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I actually just had that question myself and did some experiments. Short answer- yes. I had some higher papered mares AGA as their lower papered dams. Just a few though... the majority of them were superior. I have B/red foundations and my 2Gs are expected to be blues. Interestingly enough I had some red 2Gs that I compared to their dams for giggles and kicks and they were superior to dam despite papering red.

Papers cover a range of breeding percentages. So a Red mare could be on the lower end of that range, in the middle or at the upper end. If her Red daughter is Superior, then she is at a lower percentage than her daughter. If her daughter is AGA, then she could br slightly lower, the same or slightly better than her daughter. Remember, it's "about as good as", not exactly the same.

As far as papering better and being AGA, yes, that happens. But the better papered horse is the better horse. It tests AGA because it's just slightly better. If the parent is at the highest end of the Red range and the offspring is at the lowest end of the Blue range, with only one or a couple percentages difference, they'll be "about as good as" each other.

You can find out if you AGA Reds are better than their dams by comparing them to a known high red that is Superior to exeptionals. If you AGA's test worse than your high red, then they're likely slightly worse than their dams. If they are AGA your high red, then they are likely better than their dams. It's a lot of testing and i don't do it in my mares, only in my studs.