I don´t think the Packers will put the exclusive franchise tag on Cobb. While not likely there´s a possibility Thompson decides to use either the non-exclusive or transition tag on Randall which would allow him to negotiate with other teams once free agency starts but the Packers would have a right to match any offer.
The exclusive tag, from every instance I've seen, is pretty much reserved for elite quarterbacks. Since the non-exclusive franchise tag would require any team negotiating with Cobb to forfeit two 1st round draft picks for Cobb, it pretty much takes Cobb off the market just as effectively. No team is going to give up two 1st round picks for Cobb.