Plants take up nutrients via both the roots and the leaves. This applies to terrestrial as well as aquatic plants, but the latter tend to use leaf uptake for more nutrients than terrestrial. One obvious example is nitrogen...terrestrial plants use nitrate taken up via the roots whereas aquatic plants (most of them we keep in aquaria) take up ammonia/ammonium via the leaves. In order for plants to take up most nutrients, certainly7 those taken up by roots, the nutrient must be dissolved into water. Roots cannot take up nutrients from a dry medium.
I do not know to what extent being rooted in a substrate (sand, fine gravel, dirt, etc) differs from not being so rooted if the nutrients are all available in the water, with respect to the plant's uptake of nutrients via the roots. One primary reason for a substrate is to keep the plants anchored; sometimes the constant moving of plants can cause detrimental growth, so this is worth considering.
On a related issue, why would you not have a substrate? This is the most important biological component of an aquarium, as it is the "bed" for all sorts of species of bacteria, some of which cannot live in a filter. The substrate is in a very real sense the bedrock or basis of an aquarium, in more important ways than just being on the bottom.
