Oh I think Ozuna is unlikely, but he shouldn't be. Sure the defense will suffer, but so will opposing pitching.
Schoop is an unexciting addition that makes sense, but only if the Sox do plan on moving Kike to CF. Now Puig is an exciting addition that makes sense and may cost about the same. But then, not all excitement is good excitement, as Yasiel has proven repeatedly.
I've thrown Josh Reddick';s name out there, largele because 1) he does not suck and 2) no one seems to want him. I can't find a single rumor about him. Odd because he is a league average (maybe a tad below) hitter who plays above average defense in RF. and hits left-handed. Maybe the last two years of his reverse platoon splits have turned off anyone looking to platoon him.
But then another guy who is younger, better in the OF, and hits LH, can play CF and is a slightly ABOVE league average hitter is Brian Goodwin. Goodwin hits LHP and RHP about the same, but still could make for a decent platoon with Renfroe in RF. As could Nick Markakis, who is clearly no longer a full time OF, but unfortunately is also more likely to retire than join Boston.