Agree with BBA. By absorbing ammonia, plants can give you the false impression that your bacterial colonies in the filter are growing bigger than they really are.
Probably the simplest fishless cycle is just water and substrate, heater and filter with the lights off except when you are working in the tank taking measurements. A more extreme version (helpful in a room with a lot of sunlight) is a "blacked out fishless cycle" where you wrap the tank (with dark plastic bag material or cloth, being careful not to touch things that shouldn't be touched or to wick out water from the aquarium, which can happen any time you leave cloth or towels near aquarium tops.)
The problem, as mentioned is that Light + Ammonia triggers algae and fishless cycling sets up the ideal situation for this if light is present. The absorption of ammonia really only truely messes things up when your plant mass is very large, perhaps covering 70% of the substrate or more. But even when you only have a few plants in the tank, they need at least 4 hours of light a day and that will be enough to begin to trigger algae in many fishless cycling tanks. On the other hand, it can be said that we are describing ideals and there are certainly plenty of cases where people have fishless cycled with a few plants and not been overcome with algae, every tank is different.
~~waterdrop~~