From what I've heard Chevy say about the draft. The seventh round, even the sixth round is for individual scouts. If there is a player(s) left on the board an individual scout has passion about they will consider making that pick. If there isn't any passion they will even try and trade the pick for the next draft.
Where are they now?
Jets 6th and 7th round picks:
Jason Kasdorf (G) - ECHL
Aaron Harstad (D) - ECHL
Ryan Olsen (F) - AHL/ECHL
Jamie Phillips (G) - AHL/ECHL
Marcus Karlstrom (D) - Sweden (Div 1 = 3rd tier)
Brenden Kichton (D) - AHL
Matt Ustaski (F) - NCAA/ECHL
Pavel Kraskovsky (F) - KHL
Matteo Gennaro (F) - WHL
Sami Niku (D) - AHL/NHL
Mason Appleton (F) - AHL
Mikhail Berdin (G) - USHL
Croix Evingson (D) - NCAA
Skylar McKenzie (F) - WHL
Arvid Holm (G) - Sweden (SuperElit/SHL)
Just looking at some other teams' 6th and 7th rounders since 2011:
CBJ - Nutivaara, Anton Forsberg (Chicago's backup G)
NYI - Alan Quine
TOR - Andreas Johnsson, Sparks?
ANA - Kase, Manson
PIT - Scott Wilson
TBL - Palat, Dotchin, Nikita Gusev (KHL)
WSH - Djoos
OTT - Dzingle
DAL - Jokipakka (KHL)
SJS - DeMelo, Labanc
CHI - Hinostroza
FLA - Pakarinen
BOS - Benning
NJD - Bratt
NSH - Mazanec
I think Anaheim is winning - two very good players in Josh Manson and Ondrej Kase. Niku and Appleton from the same draft is looking pretty good too.