It depends on your water parameters and how much ferts you are adding.
It "could" if you dose very minimally and not very often. But with this scenario, the hornwort would suffer as well once it used up all the nutrients in the tank. While hornwort may be a fast grower, when you dose, it doesnt growl at the other plants and keep the ferts to itself :Angel: . However, IME, no, it does not use up all the nutrients. I have a few fast growers in my tank (anacharis, hornwort and something else - I forget). They do quite well. But, by tank is high light high tech and dose 3 times a week nutrients. The hornwort does grow somewhat quickly but it doesnt stay put (since it is not rooted). :rant2: But that is the whole point of hornwort - yes?
Good Luck
Aries