Don't think so. They will want to get that four year contract that is only allowed for first rounders. A lot of teams would love to trade up for that reason in order to pay less to a superstar in his fourth year. Maybe if the deal were really sweet they would consider it, but that also seems unlikely.
Hopefully a few "surprises" make it to the bottom of the draft. Would make it much easier to trade down if the deal was right. But your point about the 4 year deal is a very important.