Advantages of Sphagnum
Many conventional gardeners are familiar with sphagnum moss, aka sphagnum peat. It is used as a soil conditioner. Organic Gardeners are particularly fond of Sphaghum Moss. In the hydroponics realm of gardening it is also useful as a substrate / growing media.
Spaghum is a 100% natural media. It is highly absorbent, it has long strands of spongelike fibrous material that will hold and retain relatively large quantities of water without detracting from aeration and oxygenation.
Spaghnum has some advantages but also has many disadvantages in comparison to other available mediums.
Disadvantages of Sphagnum
The primary obstacles in using sphagnum is that, being 100% organic, it breaks down and decomposes over time. Small particles easily clog up your pumps. In order to maintain a reasonable level of stability with spaghnum moss, you would need to maintain a balanced sphagnum moss nutrient regimen to symbiotically coincide with your primary crop. - It's high maintenance.
Due to its high absorbency and water retention attributes over watering can be an issue. Too much moisture, too often, can easily lead to root rot.
Sphagnum moss is slightly acidic and interferes with the pH of your solution
Yes - it is possible to use sphagnum moss as a stand alone medium, the next question would be - Why ? When there are so very many more lower maintenance viable options available.
If your desire to remain completely organic is the answer to the above "Why ?" than I would suggest using it in conjunction with other more stable mediums. Vermiculite/Perlite, Light expanded clay aggregate, or even Higromite can be used as sphagnum moss partners.