The NFL is the best league in America by far. The biggest reason for that is parity. You get rid of the cap, make it so every team can go out and spend as much money as they want, you get rid of that.
You start getting team's in low-revenue markets that can't even begin to compete with other's (such as the New York teams). It truly takes away the thrill of watching the game every Sunday.
As for the Seahawks personally, of course it would be nice to be able to go out and spend money like crazy, and I'm sure that Allen would do it. The big problem though, is that their not the only team throwing that money at FA. How long before contracts got to the point of being ridiculous, ala MLB? It wouldn't take long. The NFL is the richest sport in America. The owners at the top could afford to throw 100+ million dollar contracts at players.
In the end, I think that a cap would ruin the NFL. I have almost stopped following baseball free agency because I don't want to watch players get paid $21 million a year to go out there every 5th day (pitchers obviously).
No cap = chaos.
Even if you could guarantee the Seahawks signing the guys you've mentioned, I still would never support a year with no cap.
EDIT: BTW how does a New Yorker become a Seahawk's fan????
Video games keep me sane
University of Washington Huskies: 7-6