I am going to go the other way. To me, signing Revis for '1 year' and adding players like Browner, making sure that Wilfork is still here, indicates to me that the team is in a win it all now mode. That being said, I think that Belichek might deal for Kansas City's pick. KC will want to trade back because they do not have another pick till much latter. I think this will happen only if all the quaterbacks get taken before KC's pick, because that will mean potentially 4 more great players that are available.
I live in Arizona, and all they have been talking about is Shazier at 20. I do not think Arizona takes a QB unless Bortles is still there, so if Shazier is there for KC, maybe he trades up to get him. Similarly if Clinton Dix is there he might go for him as well, though I doubt he drops that low, but you never know, if the rest of the league is QB/WR/OT crazy, might be a great way to pick a couple of defensive players that contribute immediately and forget about the 2nd and 3rd rounds. He did move up 2 years ago, to get Hightower and Jones.
If not and all the QB's drop, that means most of the 'good' players are gone, then probably someone will get desperate and trade for NE 29 pick. If available in the second round they should then consider Kelvin Benjamin, hybrid WR/TE.