Based on the in-game book, "The Firmament", it is believed that they do since it doesn't mention any special needed properties (emphasis mine):
The Warrior is the first Guardian Constellation and he protects his charges during their Seasons. The Warrior's own season is Last Seed when his Strength is needed for the harvest. His Charges are the Lady, the Steed, and the Lord. Those born under the sign of the Warrior are skilled with weapons of all kinds, but prone to short tempers.
And according to "Watcher of Stones", the standing stones only work for heroes of legend:
Long have I waited at the Guardians. I must know: are the stories true? Surely you've heard them. Tales of the stones granting powers to Heroes of old, those special few being able to choose any stone to rewrite his fate. Of course you've heard them, that's why you touch the stones as you pass by. You've heard they bring luck, or a sign from the gods. But you think little of the action. It has no true meaning for you. I see it in your eyes as you pass. You do not believe. But I have always believed. Always felt that I was one of the few whose fate was not sealed at birth by the stars overhead. One of the few who could use these stones, draw on the power of the gods to change my life, change my future. I have always felt it.
I have done much in my years. Fought battles, defended villages, quested and adventured throughout Skyrim. I have bested the Companions of Whiterun in combat, and performed deeds worthy of everlasting praise in song from the Bards College. No task was too small or great if it could bring me honor, glory, proof that I was worthy of the stones' power. And yet, nothing.