If they still had their old front office, I guarantee you they'd be doing everything they could to win this year and wouldn't even entertain the notion of trading off Bum or their relievers. Their FO is much smarter now so I think they'll be selling by mid-late July.
The NL is incredibly weird this year, though. There is only one team that is obviously 100% out of contention and they really don't have any assets that would carry much value on the market. Well, they have a couple but they are all very controllable and young so they won't be trading them. The Giants will probably sell, but I can't say that with 100% certainty. I'm not sure what the Mets are gonna do. As for the rest, I don't see any of them going into sell mode.
The AL is the opposite. There are 5 teams that are definite sellers and two more that probably should be.