Yes, and in fact that's how religion works -- the egregor of a deity becomes a vehicle for the divine power. What sets a real religion apart from the kind of thing we're discussing is that real religions are born out of religious experience: people have personal encounters with a divine power, their experiences become the template for an egregor, and the egregor becomes a meeting ground through which the divine and the human interact. In a fake religion, the egregor is created by human beings for human purposes, and the divine never comes into the picture at all.