No, your biological filter will not really help. At least not most of them on the market. Nitrate removal is handled in aquariums by bacteria called facultative anaerobes. That is fancy talk for bacteria that can function both in aerobic or anaerobic environments. Which is fancy talk for oxygen must be present or little to no oxygen can be present. The filter bacteria are pretty much all ones which need oxygen.
So we have these facultaive bacteria in our filters, but they are using oxygen and not using nirate for anything. However, If one has a planted substrate or a massive filtler such as Hamburg matten filter, there will be parts of it where the water passing through has become devoid of oxygen. The oxygen will have been used up by the ammonia and nitrite bacteria (other microorganisms will also be using O as well). When this happens, the facultative guys will switch to using what is now in the water, nitrate. And when they start doing this, one has lowered nitrate levels.
There is actually some level of denitrification happening in any biological filter with the nitrifying bacteria, but it is so litte thatitf will not be sufficient to handle enough nitrate to matter.
The thing about planted tanks is that there is a lot more to it than most realize at the outset. There is a huge difference between doing a tank with basic easy to grow stuff which requires little care vs a high light, co2 added regularly fertilized tank. As one ramp up the complexity curve, it takes greater effort and many more things can go wrong. I ran one of my dozen planted tanks in the past high light with pressurized co2 and regural dosing. After a decade I took it down. it took the most hours of weekly maint. than any other tank, and the pants were most of that. I keep plants for the benefit of my fish first and foremost and many of my tanks have no plants at all.
Planted tanks work like a
three legged stool. the plants need light, co2 and nutrients. These three things must be in balance n any given tank. If there is too little or too much of any one leg, the algae take advantage and thrive. So high light plants need more co2 and nutrients than those that do fine in lower light. getting it right is like anything else in this hobby, it takes learning and experience to master. bear in mind that ther is an additional factor, level of planting. At any light level you might plant lightly, moderately or heavily. More plants need more of the three legs than fewer plants. The best advice I offer folks new to planted tanks is the start at the easiest end and plant lightly or modertaely to start. When you get that right, start up the learning curve. It's like learning to drive. You don't start out in a Indy 500 race car because you will surely crash and burn.
What I had to learn about planted tanks was the same lesson I had to learn about medicating a tank. Unless we know what is going on, we cannot know what we should do, If we act without being on very solid ground, we will often cause more harm than good. If we are observant, both plants and fish will tell us when something is not right. With plants its clues like how do they look, are they growing are those that should do so reproducing.
Finally, I am going to send you to a siite which can provide you with a wealth of knowledge
https://tropica.com/en/