In my opinion, spirituality does lead to progress. Because spirituality is belief in what can be and not just based on the present. It is based on fantasy and imagination. In my opinion many spiritual teachings are works of great imaginations. In order to have progress the individual or group needs to dwell in the present and be thinking of the future.
I do not think that spirituality leads to progress. With the belief system many religions have embedded in their doctrine, such as the subjection of women, children, other ethnicity, and people of different religions immediately stops progress by turning a vast majority of the population into second class citizens. I also think that with the spiritual person following the mandated teachings and writings of their religion it is closing off the possibility of many scientific breakthroughs.