Hold on. I am looking at things at a pixel level. Personally for starters I've always counted Foveon's resolution at pixel level. To be fair to them I think they have as well; it was only Sigma that started the whole, we actually have 12 megapixels from a 4 megapixel CCD marketing spiel.
When I say that you get a great difference from a scanning back or a Foveon chip then I mean 12 million proper pixels not 4 million x 3.
From a group of say 12 pixels, the Foveon sensor will offer you better quality than 12 pixels from a Bayer array.
And with regards to luminance information, 12MP is 12MP yes but in certain situations there is a lot of useless information. Like I said, with a red subject for example, then if your subject is predominantly red then a lot of those Bayer pixels will not be contributing much at all.
Luminance is all well and good but there can be edging and detail that isn't betrayed by luminance values.
The original question is, is the resolution of a Bayer sensor 1/4 the stated resolution. The answer is no, but it is not the full resolution either (unlike, say, a 12mp Foveon sensor at true 12mp not the marketing spiel, if it existed). And in certain conditions for example when working with subjects predominantly of one of the Bayer colours, you suffer more.