All depends on what people sign for ... if people want to win championships then if you can get some sacrifices on what is going on ... then you have a chance.
It would appear as if the Hawks have $23M in cap space going into next season:
http://www.spotrac.com/nfl/seattle-seahawks/cap/
You know that you're going to take a good chunk of that and spread it out to Russell Wilson and Bobby Wagner. Wagner you're probably going to be looking at a deal a little richer than KJ Wright ... something in the $5M per year range would be my guess. Wilson is the wild card. I personally think that Wilson would be better off routinely signing contracts in the 3-4 year range that fit within the cap and allow for the team to surround him with the best players possible as the amount of money that he'll make outside of football is only going to increase as he continues to win at levels that have never been seen before.
Looking at this chart, Mebane is a potential cap casualty as they can pull in $5.5M into cap space if they release him. Likewise, they can pull another $5M in from the cap if they release Okung. Make these two releases and you're up to $33M in cap space before resigning Wilson/Wagner. My guess is that after resigning those two the Hawks will have somewhere in the $15-$20M range for the cap.
If you look forward to 2016 with a cap probably in the $150M range, they currently only have $77M allocated to the cap. That number will go up depending on the contracts given to Wilson, Wagner, and Lynch. But other than that, they are in a great position cap wise - particularly if they can put together a nice draft class or two together this year.
I would expect that the Hawks will sign Jermaine Kearse to something in the range of a 3 year $6-7M contract this offseason.
Bottom line is that depending on what Suh wants, it's completely doable that he could be fit in under the cap. If he's searching out $20M per year ... then of course he's not going to get it. But if he's willing to be in the $12-$15M per year (doable when you start factoring in state income taxes) and values playing close to home and for a championship contender, then it's possible.