I'd be surprised if the Seahawks re-sign Alexander. Consider that they already gave Matt Hasselbeck a $16 million signing bonus and Walter Jones around $17 million. Alexander, coming off an MVP season where he led the league in rushing and broke the record for touchdowns, is going to want somewhere in that neighborhood at least.
But Seattle's not going to give $15-$20 mil up front to a running back who doesn't catch passes, doesn't block particularly well and has that much mileage on him. They just won't (and absolutely shouldn't do it). So when they lowball him, he'll test the market. And he'll either get the big deal, or he'll find that no one else wants to tie up that much dough in a one-dimensional six-year veteran back, either.
If the latter happens, whose fault is that? It's the Seahawks' fault for franchising him in 2004 and then coaxing him into camp this year by promising not to franchise him again. Of course, he's never been the complete back that a Marshall Faulk was or a LaDainian Tomlinson is, but I would be shocked if Alexander after winning an MVP would think: "I must not be that good - that's why I didn't get the big signing bonus." It seems more likely that teams won't want to take the risk on a back with a lot of mileage, mileage he racked up getting the Seahawks to the Super Bowl (of course, Hasselbeck and Jones were more important in that regard, but Alexander, after winning the MVP, isn't likely to be convinced of that).
So after the Seahawks lowball him, if he looks elsewhere and doesn't get a deal, my guess is that he's pissed as hell about how it all went down, with his teammates getting more money and his market value diminished, and he signs elsewhere anyway.
The one counter-example here is Edgerrin James testing the market and re-upping with the Colts, but James' lower market value was also tied to his injury, not just to his mileage, and the injury wasn't the Colts' fault.
I expect this to end badly.