It's an interesting idea, but not quite by the way you proposed it.
I believe there are restrictions on sign and trading another team's free agent, so NY can't use cap space to sign and trade Amare, JJ, etc.
However, NY does want to make a splash and has no problem spending money. If they see that their capspace is not luring a big FA, and if N.O. really is looking at a terrible financial bind, because NY is so far under the cap, depending on where the cap lands, NY could could offer to give up, say, tony douglas and take back CP3, Posey, and Peja. NY would then have one legit franchise player and a legit franchise coach. They could then try and use Peja's then-expiring deal to get a longer contract but better player in return. NO, in turn, would be looking at building around Wright, Collison, Douglas, Thornton, West, and their pick this year with 30 million being just wiped off their payroll.