The presence of nitrites suggests the tank has begun to cycle, but the cycle is not complete.
If you are trying to build up a robust biological filter, in preparation for adding fish, then yes. You want to continue dosing ammonium until the fish are about ready to go in the tank. During the early stages of cycling, maintaining 2-3 ppm ammonium is probably a good approach. Eventually, though, the filter will build to the point where it's hard to maintain the concentration of ammonium because it's converted to nitrate so fast. This is a good thing, of course, because there should be no detectable traces of either ammonium or nitrite in the water when the fish go in.
So how do you know how much ammonium to add? In principle, once you've cycled, you add ammonium at the same rate your anticipated stock of fish will be putting it in the water. When this almost immediately disappears, and no nitrite is detected, the tank is ready to go. Unfortunately, I've never found handy tables for ammonium production by fish. But if you can estimate how much food the fish eat each day, you can then estimate the amount of ammonium they produce: Fish food is typically about 45% to 50% protein (except for vegetarian foods like algae wafers; they're more like 30%-35%). Let's go with 50%. On average, protein contains about 16% nitrogen. This means a gram of fish food contains about 80 milligrams of nitrogen. That's equivalent to about 300 milligrams of ammonium chloride.
I doubt I feed my fish in my 55-gallon display tank more than a couple of grams of food a day. (For rough estimating, a gram weighs about as much as a U.S. dime coin or a single strand of spaghetti.) So if I was cycling my tank to hold about that number of fish (six rainbows, four SAE, two rams, nine otos, an ancistrus, and a grouchy old clown loach), once the ammonium started to drop, I'd start working up to about 600 milligrams of ammonium chloride a day added to the tank. That's very roughly an eighth of a teaspoon. In my 55-gallon tank, that would be about 3 ppm when it first goes it, but it disappears very quickly if the cycle is up.
So it really doesn't take much ammonium chloride to keep a filter alive. And there's little harm in being generous with the ammonium chloride, other than needing to change the water more frequently to keep nitrate at a reasonable level. Your tank is much smaller than my 55 gallon, but you have live plants competing for the ammonium, so you could try 1/16 teaspoon a day as your target.
So the scheme is: Keep the ammonium level at around 2-3 ppm until you're having to add about a sixteenth of a teaspoon a day to keep the level up. Then continue adding a sixteenth of a teaspoon a day until ammonium and nitrite are undetectable within a few hours of adding the ammonium chloride. At that point, you're fully cycled and ready for fish.
If you are trying to build up a robust biological filter, in preparation for adding fish, then yes. You want to continue dosing ammonium until the fish are about ready to go in the tank. During the early stages of cycling, maintaining 2-3 ppm ammonium is probably a good approach. Eventually, though, the filter will build to the point where it's hard to maintain the concentration of ammonium because it's converted to nitrate so fast. This is a good thing, of course, because there should be no detectable traces of either ammonium or nitrite in the water when the fish go in.
So how do you know how much ammonium to add? In principle, once you've cycled, you add ammonium at the same rate your anticipated stock of fish will be putting it in the water. When this almost immediately disappears, and no nitrite is detected, the tank is ready to go. Unfortunately, I've never found handy tables for ammonium production by fish. But if you can estimate how much food the fish eat each day, you can then estimate the amount of ammonium they produce: Fish food is typically about 45% to 50% protein (except for vegetarian foods like algae wafers; they're more like 30%-35%). Let's go with 50%. On average, protein contains about 16% nitrogen. This means a gram of fish food contains about 80 milligrams of nitrogen. That's equivalent to about 300 milligrams of ammonium chloride.
I doubt I feed my fish in my 55-gallon display tank more than a couple of grams of food a day. (For rough estimating, a gram weighs about as much as a U.S. dime coin or a single strand of spaghetti.) So if I was cycling my tank to hold about that number of fish (six rainbows, four SAE, two rams, nine otos, an ancistrus, and a grouchy old clown loach), once the ammonium started to drop, I'd start working up to about 600 milligrams of ammonium chloride a day added to the tank. That's very roughly an eighth of a teaspoon. In my 55-gallon tank, that would be about 3 ppm when it first goes it, but it disappears very quickly if the cycle is up.
So it really doesn't take much ammonium chloride to keep a filter alive. And there's little harm in being generous with the ammonium chloride, other than needing to change the water more frequently to keep nitrate at a reasonable level. Your tank is much smaller than my 55 gallon, but you have live plants competing for the ammonium, so you could try 1/16 teaspoon a day as your target.
So the scheme is: Keep the ammonium level at around 2-3 ppm until you're having to add about a sixteenth of a teaspoon a day to keep the level up. Then continue adding a sixteenth of a teaspoon a day until ammonium and nitrite are undetectable within a few hours of adding the ammonium chloride. At that point, you're fully cycled and ready for fish.