No the Hawks have plenty of cap flexibility.
This off-season they will clear 10 + MM in "dead" money (3MM Bryant, 2.4MM Rice, 2.1MM Clemens + other cuts). They will probably cut a few players this off-season so let's project about 7 MM in cap savings from "dead" money.
Significant Cap increases next year:
Sherman from 3.6MM to 12.2MM
Bennett from 4MM to 8 MM
KJ Wright 1.5 MM to something higher (Not sure what signing bonus is to calculate it real quick)
also
Wilson and Wagner should both get extensions that will significantly impact the cap.
Significant Cap decreases:
Okung 11.2MM to 7.3MM
Avril 9.2 MM to something lower (I think about 6MM against the cap next year) I didn't really look at his contract yet in terms of how big his signing bonus is.
FA:
Carpenter 2.4 MM Cap hit
Williams 2MM Cap hit
Johnson 1.4 MM Cap hit
Potential cuts (after June 1st):
Lynch (7 MM in cap savings)
Okung (5MM in cap savings)
Unger (3.4 MM in cap savings)
Miller (3 MM in cap savings)
McDaniel (3 MM in cap savings)
Without factoring in the Wright/Avril extensions the Hawks salary cap going into the off-season will be at around 106MM. They also have about 2.8MM in rollover cap and will have about 30MM (+/- 3MM) in cap space this off-season. The cap should also go up again so that will give the Hawks a lot more flexibility here to something around 50MM in cap space.
Just throwing out ball park numbers:
Wilson 16 MM
Avril at about 6MM
Wright about 5 MM
Wagner 6 MM
Draft pool (I am not sure how much they will spend here. Probably similar to last year).
The Hawks will still have the cap to potentially extend Maxwell as well. Otherwise I don't think anyone else should be extended (unless I am overlooking someone). Maybe Hill (what year was he drafted? If he is eligible for an extension maybe get something done here).
If the Hawks want to keep Lynch they have the money to do so and I think they should as they don't have a good replacement on the roster.
I would also like the Hawks to address the OL/WR hole(s) and maybe a TE. Rest will be depth signings. I can see the Hawks potentially signing a key free agent even with the extensions for Wilson/Avril/Wright/Wagner. I doubt Smith gets an extension. I am not sure about Maxwell as I don't know how much he will want as a FA.
This is a rough estimate. NFL cap situation is a little confusing because of signing bonuses, partially guaranteed contracts, dead money, etc. But it should give you a rough estimate of what the cap looks like.
TBH I am really tired of listening to all the 12s on sports radio pretending they know everything about football and who will be on the team next season. Pete/John are smart and have done an incredible job in the draft (albeit the last two drafts are mehhh thus far) and in managing their cap.
For instance the 49ers and Broncos will have a lot of cap issues in the next year or two while we will not.
I just hope the Hawks can somehow sign Wilson without giving him a deal similar to Kap. Hopefully he signs a more team friendly deal (I.E., Tom Brady).