They definitely can. I've had all of my companions crit on missions and crafting. I don't have a companion with +crit for cybertech, and yet I still routinely receive earpieces with augment slots.
However, at this point in time, not all crafted items can crit. Mods and Armoring, for example, fall into that category.
That's not exactly true. Crafted items can crit one of two ways: augment slot or extra output. Crystals (from artificers), stims, medpacs, enhancements, and mods are all in the second category - companions have a chance to create an extra one. This was the case when your post was made, as well.
If I'm not mistaken, crit chance is affected by affection, regardless of whether or not that particular companion has crit chance listed as one of his/her abilities.
Goshee, thanks for making this guide, if I haven't said it already. It's been up on my toolbar for quick reference for nearly a year now, and I consult it for companion gifts and crew skills fairly frequently.