I really don't know what to expect from Dorion as the return for Karlsson. If Friedman's speculation was accurate, the package from Vegas at the deadline wasn't one that was going to help the Sens at all right now. Now you're only guaranteed Karlsson for one playoff run instead of two so that could impact his value somewhat but there could also be more teams in play now.
But he would also be free to sign an extension this summer as well meaning the acquiring team could potentially be getting him for 8 playoff runs instead of just 2, or 1 if he comes with an extension.
All that said, I really dont think the Karlsson deal is going to move the needle for the Sens significantly enough next season.
Look at the rest of that roster and even with 2-3 new good players, I dont see a playoff team. They have a downright awful Defense where Cody Ceci is the #1 without Karlsson. Even if they were to get a Dougie Hamilton in a separate deal, that still leaves Hamilton, and then some combination of Ceci/Chabot/Boroweicki/Claesson/Harpur/Wolanin filling out the rest of the Defense. Which is a tonne of either A) Inexperience, or B) Mediocre players that will play above their pay grade.
Then you still have Anderson and Condon in net. I guess it's possible Andy bounces back next season, but at 38 years old now I would say its much more likely that last year was a sign of his age catching up to him then it was a matter of some really word pattern where he's good 1 year and bad the next. Condon is Condon, basically a worse Bernier in that he can probably steal a handful of games over the course of a season, but he's going to be well below average in way more games then he steals.
They look a bit better up front then they do in net and on the back end, but still not anywhere near a playoff team I dont think. Duchene is not a #1C for a playoff caliber team. Stone is a legit 1st line Winger and Hoffman adds some solid secondary scoring, but after that, they are once again relying on a lot of mediocrity or inexperience. Is Ryan Dzingel really a 20+ goal player in the NHL going forward or was last year an anomaly for the guy who did well on a bad team with no pressure on him? And what kind of impact will Logan Brown, Colin White, Brady Tkachuk(Or if they do trade for Hamilton they wont even get that #4 pick), etc. etc. have as rookies without much insulation from the tough match-ups and minutes?
To me, looking at the Sens roster, and then looking at that Atlantic division, I just see no way they are a playoff team next year unless something absolutely crazy happens to that roster this summer that is so far out of left field nobody could even begin to anticipate it.
Boston, Toronto, and Tampa Bay are all legitimate powerhouse teams that will all only get better next year as well. Florida isn't a powerhouse team but they went on a hell of a run the 2nd half this year, and should improve next year as well.
Buffalo just added a franchise cornerstone Dman to the team(Though he may not have a huge impact on that team next season), and Montreal with a healthy Carey Price and Shea Weber will likely be back in the thick of things again also, they dont have any intentions of rebuilding or tanking right now.
They're not beating out any of those Top 3 seeds in the Atlantic which means they're fighting for 1 of the 2 wild cards. Likely fighting against Florida and Montreal from the Atlantic. Not to mention the Metro division, that will see all of Pittsburgh, Washington, Columbus, Philly, New Jersey, and Carolina likely expecting to make playoff next season as well. Three of those teams get the division seeds but that still leaves another 3 teams outside fighting for the wild card spots.
I dont think Ottawa will be better then any of those 6 teams in the Metro or the 5 mentioned in the Atlantic, not barring something out of left field.
Long story short, depending on the Karlsson trade for me will determine whether the Sens are a legit basement team in the bottom 3-4 teams, or if they end up treading water at times in the season and wind up in the ~9-13 range when all is said and done. If they get some good NHL level talent in the Karlsson deal they could improve to a 9-13 finish. If it's heavily futures based as was rumored to be coming back in the Vegas trade at the deadline, I dont see them outside of the bottom 5 again next summer.