Sorry, I had trouble opening up your images.
The short answer is yes, carefully reducing noise in the galaxy is desirable, especially in the fainter signal of spiral arms.
I have had good success using a careful stepwise approach to NR. I use MMT on the linear state of both Lum and RGB images...very carefully, with a good stretched luminance mask in place. I generally concentrate on layers 1 and 2 at this point and keep StdDev and Iterations low. There may be some noise left (which you want) but does a good job of smoothing the background and, depending on your mask, some of the fainter signal that will have noise.
Toward the end of the workflow, after stretching and enhancements, I typically do a two step process with MMT and ACDNR...MMT on layers 1-3 and ACDNR for larger scales. I use an appropriate mask for each, including a strong RangeSelection mask on those dimmer, hard to reach signal areas.
Like with most things PI, trial and error, trial and error, trial and error.......
I find this slow, stepwise NR helps control the noise in the areas you speak of, without putting too much on the background till it takes on that "waxy" appearance. You can always save the NR image separate and use PixelMath to blend it with the original, in case the NR is too much.
Joe