Sure, of course the C's can add protection to either pick. But the protection would have to stipulate what pick the other team in the trade would get if they don't get the protected pick.
Would we send the other team one if our own picks, the other Brooklyn pick, a 2nd Rd pick, or nothing? Who knows what the other team would accept. My best guess would be to protect the 1st Brooklyn pick, and if it isn't conveyed the other team gets the other Brooklyn pick (unprotected).