Adding bacterial supplement to a new tank is only useful if they have a place to colonize. This is the purpose of live rock and sand; to provide a substrate for beneficial bacteria to establish, multiply, flourish, and adjust their population based on the system's bio load. Even in a small tank, there is not enough room for bacterial colonization if you want to raise corals. It would work for fish but not for corals because fish tolerate things better than corals do.
Biofiltration is still your best option for nitrates. Even with water changes you will never be rid of all the nitrate, only the amount proportional to the water change. For example, if your nitrates read 20ppm, a 10% water change will only bring it down to 18ppm.
What kind of corals will you be growing? If your aiming for leathers, mushroom and similar softies you might be fine but you will fail with sps and other sensitive coral.
My recommendation if you absolutely will not do even very simple plumbing is doing at least a 1" live sand bed and adding plenty of live rock rubble with some type of circulation to make sure that water is flowing through the rock and sand. You can then raise your corals on egg crate for a more aesthetic effect. Use an appropriate amount of cerith snails as well especially if you will be feeding your coral. Also, an HOB filter is an excellent idea but I would not recommend bio-balls or fancy sponges. A simple sponge can be used in it to filter out large particles (changed very frequently) and a mesh bag holding carbon should sit inside the HOB filter to remove coral waste and absorb random harmful chemicals. Lastly, I believe that at least a 15-20% weekly water change is crucial for best water quality possible.
IMO a successful frag tank is very complicated and should mimic a conventional reef tank setup. My 4x2x1 shallow frag tank is actually more high tech and babied than my display tank. Still, I wish you the best of luck.
