Can you create "Versions" (as in Apple Aperture) or "Virtual Copies" (as in Lightroom) of the same image (without duplicating the entire image) in Apple's new Photos app?
Yes, you can do it several ways. With the image selected:
Pull down the Image menu, then say Duplicate 1 Photo.
Right-click or Ctrl-click the photo, then say "Duplicate 1 photo"
None of these methods make a copy of the original file on disk, a fact you can verify by subsequently saying File → Show Referenced File in Finder. No matter whether you do this to the original or the "duplicate", it always shows you the original file in the Finder window. In Lightroom parlance, it is making a "virtual copy" rather than a copy of the actual bits on disk.
That menu item only shows up when you have disabled the default preference to copy the photo into the Photos library on import. However, with that preference enabled, you can still see that the Masters sub-folder of the Photos library doesn't get a new file when you do this.
Duplicating a photo is, as you say, "cheap," but it is not free. I did some poking around inside the Photos library — which is just a specially-structured directory — and found that each duplication causes the creation of another low-res thumbnail file, plus a "modelresource" file.
The thumbnail is a JPEG version of the photo, scaled down to 1024px on the long edge. Though that's quite a bit more than what you really need for an actual "thumbnail," it's probably considerably smaller than your original photo, even if that was also a JPEG. (Even at 512 ppi, that's enough for a 2 inch "thumbnail.")
The "modelresource" file appears to be a "baked" full-res JPEG version of the original plus all of the modifications you've made to it. If the original was also a JPEG, this baked version may be either larger or smaller, so in that sense duplicating the original could be "expensive." But, if you are importing raw files, PNGs, TIFFs, etc, this file is almost certainly going to be smaller than your original file, and is thus a "cheap" copy.
It is possible that these "modelresource" files "age out" when not recently used, since it would be possible to re-generate them if Photos remembers the list of changes you've made to the original. If Photos does that, then these baked copies behaves similarly to Lightroom's "catalog previews" database.
Bottom line, making duplicates of your master photos will cause the library to grow, but not as fast as if you import multiple on-disk copies of the same photo.