Athough I think the Red Sox have tried to upstage the Pats in the past, I do think the recent trade and signing is pure coincidence.
In the past, the Red Sox hate sharing the media spot light with the Pats and act like that child who demands attention from Mom and Dad all the time and when another of his/her siblings gets attentention, he/she forces hin/herself infront of the sibling to get the spotlight again. This doesn't seem to be the case.
I think the current moves themselves is an attempt to regain the spotlight, but not steal the thunder. The Sox brass see that the public interest is definitely shifting from the Pats and onto the Pats, Celts, and Bruins. The ratings are down. Attendance is down (they sell out, but there are a lot of empty seats in the stands losing concession sales). Patriots talk dominate the airwaves even in the summer. The Sox are definitely trying to make themselves relevant and a hot topic, but they are more concerned about their long term interest rather than steal the Pats' spotlight after the Jets' win.