In Magic: The Gathering, can I include a card in my deck that I can't play based on my land setup?
If you are playing a typical constructed game, there is nothing that stops you from putting Progenitus in your deck even if you don't have anything that will give you the mana required to cast it. The Magic Tournament Rules for constructed tournaments don't have such restrictions: Deck Construction Restrictions.

On the other hand, there are formats which won't allow you to put Progenitus in your deck, unless specific conditions are met. One example is Commander, where you would need a Commander of all colors (or make Progenitus your Commander).