At least from the Buddhist side of things (and in more than one Buddhist tradition), the spiritual path consists roughly of:
1) an initial awakening to the true nature of one's own self-construct
2) a lifelong process of deepening and integrating this deeply liberating insight into all aspects of one's mind, life, and behavior
The Buddhist canon contains a lot of stories about people who attained at lease a glimpse of 1), sometimes seemingly triggered by a random event (especially in the Chan/Zen tradition) such as hearing a loud shout. So I wouldn't be surprised if psychedelics could drop-kick one's consciousness into this realization.
But I would be surprised if drugs alone could produce the kind of long-lasting shift in perspective and well-being that 2) brings - mainly because it requires a lot of meditative effort, and effects of pharmaceuticals tend to be transient.