Can the NHL suspend or fine a player for a dive if they weren't penalized for it during the game?
Yes they can.
64.3 Fines and Suspensions - Regardless if a minor penalty for diving / embellishment is called, Hockey Operations will review game videos and assess fines to players or goalkeepers who dive or embellish a fall or a reaction, or who feign injury. See also Rule 28 – Supplementary Discipline. The call on the ice by the Referee is totally independent of supplementary discipline.
The only heaven I'll be sent to is when I'm alone with you
No ****. Is that new this year? I don't remember language about faking an injury in the rb before.
I'm not sure if the language is new, but I know the bit about the league being able to fine a player for diving or embellishing even without a minor called in the game has been in the rulebook for a while.
Corey Perry did something similar in the 2007 playoffs I believe. He skated into Chris Chelios from behind and faked getting hit to get an interference call.
I dont think perry has a bad rep for embellishing calls, tho he does give the refs stares and arms out to try and draw calls. Bobby ryan and teemu selanne seem to embellish a lot tho, i think they are pretty underrated in that part of their games.