Yes low levels of ammonia, nitrite & nitrate do help fish fry to grow better.
Good fin development is more about clean water reducing disease organisms, and the genetic make up of the fish involved.
fish fry & young fish should be kept in clean water until they are mature to prevent stunted growth. When they are adults they will be fully grown (or close to it) and they should no longer be growing their fins. Low nitrates are better for all fish but more important to young fish.
Having nitrate removers in the filter/ tank will only help keep the nitrates down. This will help the fish do better but won't necessarily help them grow any faster. Fry grow best when kept warm, are well fed, and have clean water. Daily water changes are the best thing for growing fish fast because it dilutes nutrients, helps keep the PH stabile, dilutes disease organisms, and dilutes hormones that are released by the growing fry.
Although nitrate removers help by keeping the nitrates low, they don't do anything for the other points, in particular the hormones from the baby fish. Carbon can be used for this purpose but should be replaced regularly.
What are the Pros and Cons of Nitrate removers?
Pros, low nitrates
Cons, can be expensive
There are de-nitrating filters that cost a bit to buy but are cheaper to maintain in the long run. They work like a biological filter but become anaerobic instead of aerobic. Tank water flows through them very slowly and the bacteria eat the nitrates and convert them into nitrogen gas that then gets expelled from the water.
However, as mentioned, plants do a great job at removing nitrates. Fast growing surface plants like Water Sprite and duckweed do a great job at sucking up nutrients. If you remove some of the plants on a regular basis you then remove the nutrients from the tank and lower the nitrates.
Water changes are a very effective way to lower nitrates unless you have nitrates in the tap water. Then you are fighting a losing battle and need to use plants or de-nitrating filters.