As anonapersona indicated, the effect of plants is highly variable depending on the conditions and the plants.
Plants do not really speed the cycle as much as they bypass it. Healthy actively growing plants will uptake ammonia for their own use, so that part of the tank-generated ammonia never feeds the bacteria and is not converted to nitrite. If you have enough plants and the right light/CO2/ non-nitrogen supplements, etc, your plants will out-compete the bacteria, but the bottom line is reduced ammonia titer, no nitrite, no nitrate.
But if there are too few plants, incorrect light, no nutrient balance - then the plants will do little or nothing.
If the plants are unhealthy and degenerating, they will contribute to ammonia/nitrite/nitrate.