Yes; plants require macronutrients and micronutrients. We need to provide three macronutrients (nitrogen, phosphorus and potassium) to plants in order for them to grow.
Without these nutrients, plants will not do well.
For more information regarding fertilization and plant well being, please take a look at my guide to planted aquariums, linked in my signature below.
Sorry, I meant to say that since fish already produce N and p, would it change the growth rate much?