No chance that Finley is traded, it isn't a matter of if he has trade value(he does) its a matter of keeping your talented players, Finley is a top 5 TE(even with the drops) and you don't trade away players that good that you've just resigned. Finley is a young guy and his career is still very much on the upswing, he has the potential to be the best TE in the league, you don't give up on guys with the potential to be the best at their position. The Packers were ready to franchise Finley, that says a LOT about what they think of him.
I think its reasonable to say that the Packer's likely see Finely's value as higher than what they would get in a trade for him. You really have to look at the history of trades to understand this, how often do teams trade away young players who are under contract with huge potential? Most trades happen because a player is under performing, a malcontent, has a huge contract, etc etc.
You also have to remember that trading players for picks is extremely risky, on one hand you know exactly what you have with a player, and on the other hand, the draft is a complete crap shoot. Sure I would trade Finley for a draft pick if it meant I would get another Clay Mathews, but any idiot can look smart making draft picks in hindsight, in reality it just doesn't work that way.
I will go out on a limb and say the packers will not trade *any* starter for draft picks. Any trades will be for picks(very likely) or backup/role players(less likely). I think the last player Ted Thompson traded on draft day was Javon Walker(again with the malcontent thing). I also don't see GB making a huge trade up in the first, you have to give up too many high picks to make that happen, moving up past 20 is likely out of the question.
Again nobody is saying Finley doesn't have trade value, or that DE and OLB aren't huge needs, but thinking you can pull off these magical trades and everything will just fall into place isn't realistic at all.