Yes, the Bluefly shoes come with the original box, as do the scarves, etc. when you buy them there. Not sure about "big bags" like the occasional travel Birkin or HAC they have.
If they did not have the original box, of course they could and would ship the shoes in a shoebox-size mailer (just like eBay sellers do)--but they do have the box in my experience.
At the sale, I do think they come with the box as well. At least, mine did.