From my experience, no. I haven't sold anything on eBay in months, but yrs ago when I first started out selling I shipped things in similar type boxes if they were the perfect size or cut down a box to the correct size. I have a couple of old reviews, which may not be "read-able" anymore, where the buyer remarked on my box or packing, saying it was an imaginative shipping box and so well wrapped nothing was getting out. I may have overdone the newspaper for safety's sake, most boxes had a brown paper bag wrapped over it, which I used to write the address on in black marker, and plenty of clear shipping tape around and around the box. From my experience, they got a kick out of it, never a bad feed back. I think it just matters if it looks like you made a really good effort to get it there in good shape.
T.