This will work, though plant growth will likely be less than in a fish tank. I have a 20g that is my QT for new fish, and I keep it running permanently with plants culled from the other tanks. Right now it has been maybe 3 or 4 months without fish, and previously I have had it running for half a year or more without fish. I dose Flourish Comp 3 times weekly and do regular weekly water changes of 1/3 the tank just to keep it fresh, but I do not use water conditioner as there are no fish and plants will take up the chlorine.
I dose FC three times but that is because all my tanks get the same. I have very soft water and found that I need more than just once or even twice weekly.
I have noticed that the plants remain green and healthy, but they do not grow as fast--less spread on floaters, fewer runners on chain swords, etc.
Remember there is some nitrogen (= ammonium and nitrate) in Flourish Comp. Plus, you would be amazed at the amount of detritus that collects in the substrate even with no fish. I still don't know where it all comes from.
Some is undoubtedly plant leaves that have fallen off and not been noticed. And I do have snails in this tank, Malaysian Livebearing and pond.