Underhill: I think everyone involved knows Carr cannot play this year at his current salary

That's your opinion though.

What if Carr tells this to the Saints brass, and they actually like the player (which based on previous year's tea leaves, they do) and would be willing to make moves to accommodate?

I mean, you yourself would do the tough guy thing with Carr, but the Saints front office itself may not have that same mindset.
I don' think the Saints see Carr as part of the future of this team. They would not invest heavily in an aging WR just to appease him. He is not in a position of power to dictate personnel moves at this stage in his career and position with the organization.