Do you need internet for streetpass on the 3DS?

Yes, it does. However, if you have friends on the 3DS friend list, they will be able to see you are offline.

Referal via streetpass, you close the 3DS with the power still on. IF you walk past tons of people, one of these people might have a 3DS. BAM! if you walk past each other, your personal mii will go into the other person's plaza, therefore you will have a hero for find mii, person to trade puzzle pieces with, etc.