The regular season opener for the Sox is on a Monday afternoon - and, in fact, is smack dab in the middle of the Bruins brief break.
The regular season home opener for the Sox is similarly Monday afternoon - and is in the few days between regular season hockey and playoff hocke. Again, no conflict.
The games against the Caps and the Panthers, however, do conflict. I'd wager that the Bruins get NESN iff the WC spot hasn't been clinched. But if the Bruins are either already in the playoffs or already out of the playoffs, I can see them being relegated to NESN+. It's tough to manufacture excitement when you've got Svedberg in net, and you're benching Bergeron and/or Chara because of, as Jack Edwards put it last year, a "broken mahnamana".
As far as any potential first-round playoff games, there's no way that those get shuttled to NESN+ for Red Sox - and I'm sure John Henry had a nice long talk with the MLB schedule maker to make sure that no Yankees games were scheduled in late April.