Do PlayStation Plus cloud saves automatically update?

Yes, they do automatically update. This feature was introduced in firmware update 3.70 which is super cool :)

Source

and one or two more, just to make sure.

Yes. The playstation blog has a breakdown of the firmware release that included cloud auto saves.

http://blog.us.playstation.com/2011/08/09/ps3-system-software-update-v3-70/