My answer to the question is yes. I have personally experimented (not voluntarily) conscious dreams a few years ago.To be more precise, I was conscious in dreams but also conscious to dream.
Of course this answer is a testimony, not a scientific proof, of the existence of conscious dream.
But maybe in cognitive science, many serious testimonies constitute a proof.
Let me add an interesting remark and a question:
As I said, the processes of consciousness and dream seem to coexist, but as water and oil, they tend to separate quickly:
In my experiments, when the process of consciousness started in a dream, then the dream becomes increasingly blurred and awakening occurs rapidly.
I remember to have consciously walked and explored my dreams worlds for a few minutes or quarter of an hour (to be more precise, it seemed to have had this time), but not more ...
Is there a cognitive explanation for this quick separation ?
To make a nod to the Indian philosophy (@SaiKrishna):
Consciousness is light and dream is shadow.
When the light encounters the shadow, the shadow disappears...