I cleaned this thread up and deleted everything that wasn't explaining what an AA-filter is/does.
A 36Mp image, filtered and properly downsampled to 12Mp will be sharper and less susceptible to Moire patterns than an original 12Mp image. The downsampling will also decrease the noise a tad, but I have no idea if that would be comparable to the noise on the original 12Mp image.
I think you are trying to mix bleach with apple juice to get lemon-aid.
Everyone on here seems to understand that AA filters reduce moire that is an optical phenomenon. Chromatic abrasion also can add/create moire as well.
Now it seems that this is going into using software to reduce it. Down-sampling will not necessarily reduce noise or moire. It can, but it also can make it worse or blur the image to correct it as well.
Moire happens when frequencies start to converge which is a basic end effect of Regular Rectangular Patterns on sensors. Computers work in 1 & 0s and has a regular pattern as well so that is why software solutions are haphazard as well. All of it is better solved with physical design then software. The physical design fix so far is only to use an AA filter which blurs the sharp edges of the image slightly. If you have ever seen a 6mp dslr with with AA removed you can really tell the difference, but now not so much.
Two ways to correct: Go to a Sigma Foveon type sensor which has proven it reduces moire to an indeterminable amount. The second is to capture the light detail at such a fine level the eye can no longer discern (recognize) it. It will exist though, but as such a small level, it will not be noticeable. This is what companies seem to be moving to as (among other things) utilizing as a solution.
I'm not sure if 36mp is at that point or not - we will have to see that.
Noise on the other hand with increase mp will get worse (that is solvable by software) as that is produced by the "wells" not receiving enough light to properly record the color. Software improve noise using algorithmic calculations based on the recorded color values of adjacent pixels. The issue arises when those also did not record good color values. That is why having larger wells which capture more light is preferable. This calculation could as a result reduce moire but that is not the objective of the procedure and is just a secondary result of the process.