No.

Martin cannot be traded, iirc. He has to go back on waivers.

He absolutely can be traded Edmonton would have to keep him in the NHL. He'd only have to be offered back if Edmonton tried to send him down. See Mikey Eyssimont last season. San Jose Claimed him then traded him to TB at the TDL.

Checkmate

I think the difference is that Eyssimont had already cleared waivers earlier in the year. Martin has not cleared waivers this year and I think would have to before we could trade him.

Nope as long as they don't send him to the minors he doesn't have to be offered back. The purpose is to prevent a team from claiming and burying a player.

A perfect example of the reason behind it Alex Barre-Boulet
Seattle claimed him then wanted to send him down so they placed him back on waivers when no one else claimed him TB then reclaimed him and was able to send him down.

Regardless of the Spencer Martin waivers issue, I don't think it's realistic. The 2nd would be enough for Roslovic with retention, the Edmonton 2024 1st is about right to move Campbell's full deal, but Martin + 5th < Akey IMO.

So not only does the deal favor Columbus (so EDM likely declines), CBJ still say no because now the goalie tandem is two $5M+ goalies who have historically waaaay underperformed, on the books for a concerningly long time.