i bought my van from ebay it was a bit strange not really checking it over or even starting it. but it turn out to be fine no problems in over 6 months.
i have also sold my old van on there the bloke picked it up without really looking at it i wound not have a problem if he wanted to see if it was as i described.
If i asked for it to be started and the seller wouldn't i would walk away. thinking you must be hiding something.