No, diatoms feed off of silicates and nitrates. You will always have nitrates as they are the final end of the nitrate cycle.
If you have diatoms, all it means is that you have silicates. They most often show up at the end of your cycle because it is finally habitable for life and they are feeding on the higher silicates that are present in new rocks and sand. When that is used up in a few weeks, they go away. If you are using tap water you many never see them go away because many tap water sources contain silicates.
Seeing diatoms is handy indicator that your cycle is over, but it is not a positive indication that your tank is cycling or has cycled.
So, you should put some food, either flaked or frozen, into your tank to see if it is cycled or not. That is the only way to tell. If you see no spikes in level, tank is cycled, if you do see levels of ammonia or nitrite, you arent done cycling yet