Is it possible to perform an action on a number of photos in Lightroom; e.g., applying noise reduction using a plug-in such as NikSoftware's DFine?

Any number of Lightroom settings can be saved and applied as a one-click preset. White Balance, Noise Reduction, Sharpening, Crop, Lens Correction, etc. could all be in a single preset. And that preset can be optionally assigned as the default for all incoming images if you want everything to come in with a certain "look" before you even touch them.

I don't use plug-ins, so I don't know if plug-ins can be part of presets. I'll bet they can, but don't quote me on that...

In addition you can take the hero image you worked on, the image that has edits you want to use elsewhere and simply copy and paste them to other images you select on the grid. Also look into AutoSync. There are many, many different ways of doing what you wish. The joy of LR! As far as the plug-ins like NIK, the problem is they have to render out the data to an actual file to apply their effects, which greatly defeats the usefulness of metadata editing. You might as well apply this in Photoshop on a TIFF file (that’s what the LR plug-in’s do anyway, all in the bkgnd).

Plugins like Nik's can't be included in a preset because of the behavior Andrew describes. If there are particular settings you apply to all raw images you can use them to customize the default settings applied to all raw images you import in the future.