Even the Navy NGs (C40) have HUDs.
No you can't go down to CAT IIIC levels because there's no rollout capability (manual rudder only) on the 737. I'm surprised that Alaska even lets you go down to 600RVR and no DH whatsoever? Sounds kind of dangerous without rollout.
Even if you've got a good autoland the HUD is still useful during low vis takeoffs.
There are no "daily autoland checks" - monthly I believe is the most stringent.