A DNG image is a format that Adobe created as an umbrella format for all raw images. Generally raw images are proprietary to each camera manufacturer's design. As such Adobe has to reverse engineer each one to avoid copyright issues. Raw images are especially unique image types and vastly different from TIFF, PSD, or JPG, GIF, or PNG image formats.
I suppose one might look at beans, meat, onions, garlic, and various chilies and spices to make a pot of chili. What you're asking is is it possible to take a pot of chili and turn it into beans, meant, onions, garlic, and various chilies and spices.
The answeer to that is no.
HOWEVER, you can use both Lightroom and ACR to work with TIFF, JPG, and other image types with the same tools that you use on raw/DNG images.
Much like TIFF, DNG is owned and controlled by Adobe, it's a container for data. A DNG may contain raw data but it can contain a JPEG, etc. So the first thing is, why do you want to use DNG for anything other than raw data? If no, then sure, you can convert proprietary raws to DNG and there are some advantages and a few disadvantages of the format. As for Photoshop, it will treat a DNG by using Adobe Camera Raw. Is that what you desire? Camera Raw does it's edits using instructions (parametric edits) which are then turned into RGB pixels when you finish and tell ACR to 'open' that as an RGB document in Photoshop. Photoshop edits RGB (and similar color models) by altering the values if pixels which is a bit different than parametric editing.
So we need more information about what you hope to do, where and why before going farther into DNG vs. PSD (or better IMHO, TIFF) inside Photoshop.