Can I get the same results by copying a RAW (same exposure) file many times and stacking to reduce noise as I would if I used many separate exposures?
No. If you stack copies of the same image, you'll amplify the noise right along with the signal.
Stacking images to reduce noise is an averaging process. It's like a science experiment: you don't measure something just once, you measure it multiple times and average the measurements to reduce the effects of error in the measurement process. Doing what you propose would be like taking just one measurement and writing it down in your lab notebook several times.
When you take an image, you're measuring light intensity at every point on the sensor, and noise is essentially the error in each of those measurements. Because the error is random, it changes from one exposure to the next. For two adjacent photosites, the data recorded across 5 exposures on a 0-255 scale might be:
Adding those up and dividing by 5, the average value for both photosites is 148. Averaging the values over several exposures smooths out the data, eliminating the noise in each photosite. Even though the individual measurements for the two photosites are a little different, they both have similar averages because they're both recording the same part of the scene.
Now consider what would happen if you stacked multiple copies of the first exposure:
Now you're not removing any noise at all -- the averages are 150 and 152 respectively. You get exactly the same degree of noise that's present in the image that you used.
You cannot. Removing noise via photo stacking works on the principle that the noise in your images is random, and appears in different places of the image between exposures. When you stack multiple exposures on top of each other, a common method to remove this random noise is called median blending. During this process, software will evaluate the same pixel in each version of the image, find the median value, and assume that is the true color value of the pixel since the random noise values should not be near the median of the pixel's color distribution.
When you stack multiple copies of the same exposure, your noise is going to be in the same exact location in each copy, and thus cannot be removed via this method. There are however noise reduction tools that will attempt to remove noise from a single exposure of an image.
One possibility might work and be what you say: the same RAW exposure processed different ways using RAW-processing tools, to bring out different parts of the image. E.g. tge background may have its exposure boosted ans be run through a plug-in advanced noise reducer, while the foreground has different white balance, lower standard NR, but a touch of smoothing.
If the RAW-processing tool doesn't have regional editing or layers, or you're actually using different programs for different parts of the image, then you can bring them in as layers in the photo-editing program for final compositing.
Or course that's not the same as the layer-averaging tool you were implying.