1) Matt Hasselbeck
No player might be effected more by this rule that Hasselbeck. This would be a nearly ideal situation for the Seahawks. They could explore all their options while letting Hasselbeck shop until his heart's content. Teams would still kick the tires, but they'd likely be less interested than if they could sign him outright. You can see why the NFL Players Association is not keen on this rule.
2) Brandon Mebane
More manna from heaven for the Seahawks as the team can put feelers out on alternative DT options knowing they have Mebane locked in should they want him.
3) Kelly Jennings
Kidding! Sad to say that I'm not sure there is another free agent that the Seahawks would apply this rule to. Leon Washington would have been a possibility, but he already re-signed. Will Herring could be due to the lack of experienced depth at linebacker. The only guy who might qualify for this would be Raheem Brock. I don't know the Seahawks would be likely to match in his case, but they may prefer to have the right to do so.
That's the good news. The bad news is this would reduce the number of options for the Seahawks. It is not clear which free agents would be eligible to have this tag applied, but if it's any free agent, we might see the Raiders apply it to Robert Gallery. Minnesota might apply it to Sidney Rice. The wiggle room in negotiation on this might be the number of players owners can apply it to. Seahawks fan may want to hope this rule is enacted, but can only be applied to one player. This would give the team a great chance to sign either Hasselbeck or Mebane while also having enough quality players available in free agency that they could fill in some important gaps.