Well, that's not 100% true..
For chip containment, some clear plastic shields on magnetic bases work wonders at protecting you and the stuff around the mill. Makes clean up alot easier too, especially if you cover the exposed T-slots on your mill table.
For your spacer, be aware that the act of clamping it to the table may bow it, depending on where it's clamped and how tightly. You may need to do the uncut surface and then turn it back over and lightly skim cut the surface you cut first. Do you have a way of surveying the thickness of the spacer on your surface plate?