Could Derek Carr be a post-June 1 cut?

As @Rouxble pointed out, Carr was contract inflexible with LVR. Zero reason to think he helps us.

Carr has a “no trade” clause. The only route would be Carr agreeing to salary being converted to option/roster bonuses and us asking Tenn/NYG if they want a mentor for the rookie QB they draft for a 7th and Carr agreeing to that all before the 3rd day of the league year. That still leaves us 40M and 11M dead cap over the next two years. We can’t cap manage a 40M dead cap hit. Finding great value at QB is a route to winning. Carr isn’t great value. Loomis overpaid with the 20M in roster bonuses and “no trade clause”.
The theory is he would do it to help himself get in a better situation, not help the Saints out. But like I said they'd need to be another team out there willing to cover his base salary (BEFORE FREE AGENCY START), very unlikely.

I don't see any situation where Carr helps facilitate a trade for even a 7th round pick.