"Cycling" a tank refers to establishing bacterial colonies in the tank with species of bacteria that convert ammonia to nitrite, then other species which convert that nitrite to nitrate.
I would argue that "cycling" refers to establishing bacterial colonies in tanks where the bacterial colonies
are the primary of converting ammonia to nitrate. In my heavy planted tanks the ammonia never builds to a point that triggers the rest of the "cycle". Sure the colonies are there in the filter and on the plants but they are not the only thing keeping my fish alive.
Packing in the healthy plants is also a good way to limit algae in my experience.