The real question isn't about the bodies, since human remains would make good fertilizer. Rather the issue wold be the mechanism of death.
If the battle took place in ancient times, with the proximate cause of death being through edged weapons or blunt force trauma, then plant growth would be able to take place right away. The main issue would be the bodies would cover the ground and prevent plant growth where they lay until the remains were fully decayed, or scavengers ate them. In most instances, the bodies were stripped of armour and valuables and then buried, which would facilitate plant growth even better since there would not be a large quantity of metals or other inorganic materials to interfere with plant growth.
If the battle took place during the age of black powder warfare, the situation would be relatively similar, but there would be additional complications due to the quantities of inorganic materials embedded in the ground in the form of spent bullets and shells or pieces of shrapnel. Gnerally speaking, this would be localized in small areas, and if the water table was high, then lead and other compounds could leach into the groundwater and stunt some of the plant growth.
The battlefields of the Western Front during the Great War of 1914-1918 would have a much different issue, as the ground was churned up by massive quantities of artillery focused on very small areas of ground. Not only will there be a lot of contamination of the soil, but the very structure of the soil will be changed. Explosive shells would turn the soil and bring clay and other materials from deep below the surface; materials which is missing much of the organic matter needed for plant growth. The natural drainage would also be disrupted or destroyed, making plant growth more difficult as well. Use of chemical munitions will add complications to the regrowth of vegetation as well, either directly or indirectly as animals and insects which are beneficial to plant growth avoid the contaminated areas.
More modern warfare can have much more firepower, but the general trend has been to spread things out over a larger area through mechanization, as well as using more precise munitions to target things, so unless chemical munitions, nuclear weapons or biological warfare is unleashed, the effects of modern warfare on vegetation is very localized and diffused.