yes if you save a process icon from STF before the stretch, you should be able to drag that onto HT. if for some reason that doesn't work, you can always double-click the saved STF icon which will re-load the STF process with the old parameters, drag STF's triangle to the HT control bar at the bottom, and then apply HT to the NRed image.
another way to do it would be to copy the STF settings to HT before doing the NR, and then after the NR apply the HT process.
there is no way to copy STF's settings to masked stretch (or other stretching processes) because they work very differently. STF just sets the midtone transfer point and the black clipping and those are concepts that the HT tool understands. while the other stretching tools do similar stuff i guess the "how" is different enough that a fixed midtone and black point don't mean that much to them.
rob