Not sure because while SD drafted Manning and NY drafted Rivers they were both traded on draft day. Not sure if something like this could happen.
Let's look at it this way. Without going outside the box, to create the scenario in advance.
Assume on June 2nd, the Packers see a guy that was drafted by the Mud Hens in the first round that they actually wanted. Assume he has yet to sign his rookie contract. Now, let's say that the Mud Hens would be more than happy to trade this guy they drafted for the rights to Rodgers. So, they make the trade, and the Packers sign this guy after they've received the rights to negotiate with him. That's totally legitimate.
Now, in my scenario, the only thing that has changed is that both teams agree in advance of the draft that they will specifically do something. The Mud Hens agree to draft the player the Packers want. Then, they will hold off on negotiations on his contract until after June 1. At that point, they offer the rights to him to the Packers, in return for Rodgers. The trade is made. Now, understand that whether or not the suggested trade will ever take place or not will hinge on the team actually being able to pick that player in the draft. If he's gone already, the deal is nullified.
The only thing different between the two scenarios is that an agreement to a trade has been made "in principle" between the two teams, and has only been discussed, not made. The decision to make the trade official comes after June 1, officially. For all intents and purposes, until that point, it's all speculation and nothing more than discussing a potential trade.
So, as I've been stating all along, you can finagle trades through certain methods, without actually breaching the NFL agreement on them, and at the same time, do it through means that are somewhat devious, because you've worked the system.