I see that many legendaries have 'unique on equip'. I understand this means I can't use 2 of them at the same time, but what happens if I have one already (say in stash) and find another one of the same item, can I pick it up?
Yes, you can pick it up.
The restriction only applies to when it is equipped. If you have one equipped, and another drops, you can grab it but not equip it.
Seems very unlikely this would happen though.