Is the head angle on full suspension bikes given with or without sag? Is the head angle on a full suspension mountain bike measured with our without sag? I would imagine that the rear shock sagging would give a slacker head angle than what is measured without sag.

Generally they are measured unsagged. Usually, as @alex said, it doesn't matter, since they are full suspension bikes, but some setup (e.g setup for super steep races) where you want your rear end softer, it would matter.

Some hardcore hardtails (e.g the blue pig of < measure the head angle in a sagged situation. Because they are hardtails they only nose dive under the rider's weight.