The Ecclesiarchy is one of the pillars of the Imperium, yes. I personally used to travel with a priest myself. Quite a dirty old rogue, but he ministered to our men, particularly the dead and dying. We loved him for it.
[He nods.]
Yes, we have been traveling between the stars for over 30,000 years. Possibly more. The regards from times before the Dark Ages of technology are... sketchy at best.