They are still shielded and the increased integrity remains. I've did it mostly with afmu's since i power them only when i disable the thrusters^^
If powered off, the shielded afmu's have still their increased integrity and can't be destroyed (hull breaks faster). I've tested it some time ago (2.2 ?) With a friend and i don't think that it got changed since that.
I can't suggest it on pointdefense because they get more integrity through reinforced blueprint and they can still remain in prio 1 below 40% powerdraw in most builds.