Can you get armour for your shapeshifted forms?

Not quite sure what you mean.
Whilst shapshifted you continue to gain the effects of the armour that you are wearing it's just not displayed. Cat gives the same armour, Bear 180%, Dire Bear and Moonkin 360%.
All the stat bonuses of the armour are still active as well. Hope this helps.

I suspect he means if we can visually see armor on the forms, and the answer is no, although that would be pretty cool.

Correct. You can get higher AC leather gear, which will increase your armor in forms. Though you can't get armor which shows up on your toon. Which would be insanely cool. Bear with some kind of fist weapons?