Depends on the draft year naturally. I attended the 2017 Draft, so I didn't bother rewatching some of the footage until the recent Bobby Clarke comments. Both Darren Dreger and Bob McKenzie said that the Devils were entertaining the idea of trading down to #3 and that Vegas was trying to pull off an elaborate set of trades that would have garnered them the #1 pick. Presumably, Vegas wanted Nolan Patrick and the Devils were okay with whoever remained between Nico Hischier and Cale Makar at #3 if they got enough to move down. It sounded like Dallas had no interest in moving from #3 to #6, so it never came to fruition.
Florida listened on offers for the Aaron Ekblad pick in 2014:
Flyers were 'close' to trading up to No. 1 for Aaron Ekblad
Rick Dudley got creative the three times he had the #1 overall pick. Although in each case, he traded down and ended up with the guy he would have taken #1 anyways. That might not apply with the 2022 Draft.
1999: Dudley was GM in Tampa. He was planning on taking Pavel Brendl with the top pick but knew that Brian Burke badly wanted both Sedins. Dudley offered to trade #1 for #4 plus 2nd and 4th rounders. Oddly Burke considered that to be too high a price. On the morning of the draft, Dudley relented and accepted Burke's offer of a pair of 3rd rounders. In Dudley's eyes, he was getting the player he would have taken anyways plus a couple picks. Dudley would then trade the Brendl pick to the Rangers.
2002: Dudley was now GM in Florida and planned on taking Jay Bouwmeester #1. Columbus was picking #3 and wanted Rick Nash but got scared as Philadelphia traded up to #4 on the morning of the draft. They were worried that Philadelphia might swap that pick with Atlanta at #2 and take Nash. Most figured Atlanta was taking Kari Lehtonen or Joni Pitkanen, so they would get one of them at #4. Columbus GM Doug MacLean called up Dudley about swapping picks and they figured out an interesting swap. Columbus gave Dudley the option of swapping 2003 1st round picks, ie Columbus used its presumed lottery odds as an asset. In the end Columbus didn't give up anything in order to secure Nash. Dudley had to give Atlanta an extra pick to promise not to take Bouwmeester at #2 and Florida got Bouwmeester at #3.
2003: Florida won the lottery and had Nathan Horton at the top of their board. Dudley figured they could move down a spot or two and still get Horton. So he shamelessly tried to create a bidding war between Carolina and Pittsburgh. In the end he got a modest return in exchange for swapping #1 for #3.
And then there was the Islanders trading away the Jason Spezza pick in 2001 as they wanted some immediate help.
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If the Devils lucked out and got the #1 pick, Arizona and Montreal would be natural trade partners at #2-4. Coyotes and Canadiens both have a ton of picks. Extra incentive with the draft being in Montreal and it being Kent Hughes' 1st draft as GM. Currently at their disposal:
Arizona: ARZ1 (2nd-4th overall), CAR1 (~30th overall), COL (~30th overall), ARZ2 (~33rd overall), PHI2 (~38th overall), SJS2 (~43rd overall), NYI2 (~44th overall), ARZ3 (~65th overall)
Montreal: MON1 (2nd-4th overall), CGY1 (~30th overall), MON2 (~34th overall), EDM2 (~50th overall), MON3 (~66th overall)
Devils could trade down a couple spots and take Slafkovsky/Nemec/Jiricek then add an extra pick that could be used to trade for immediate help.
Although trading for it for NHL bodies does remind me a bit of the 1999 Draft and Dudley turned the top pick into not a whole lot:
1st = 4th overall + two third rounders
4th overall = Niklas Sundstrom, Dan Cloutier, future 1st rounder
Sundstrom = Andrei Zyuzin plus warm bodies
Dudley thought he was getting his goalie of the present/future in Cloutier, a young former 2nd overall pick in Zyuzin, and another first rounder for his one pick.