You can add plants at any point in the cycle, the high nutrients won't bother them at all. They may slow the cycle down a bit, though, as they will take up some of the nutrients in the water. The flip side of this is that the plants can be a significant portion of your biological filter, particularly if the tank is heavily planted and the plants are actively growing. You can actually do what is called a "silent cycle", by planting the tank heavily right from the start, and once the plants are growing well, add fish slowly; the plants will take up the extra nutrients produced by the fish while the biofilter gets established. Key here is the tank must be heavily planted right away and the plants need to be happy and growing, otherwise they will not be able to adequately perform their nutrient uptake duties.
I find that it is actually more difficult to plant when the water level is low as the plants fall over and you can't see anything. Unless it is a very deep tank where you physically can't reach the bottom unless the water level is lowered I would go ahead and plant with the tank full. Once you get the tank established you'll have your arms in there frequently for trimming and replanting anyway.