The guy that's killing us right now is Darnell McDonald.
So rather than asking "If Ells is out for X amount of time, should we go get someone in a trade", it's more of a "Crawford will be back in 2-3 weeks, the schedule goes from extremely difficult to extremely manageable starting a week from today. Can we manage without Ells and Crawford for the next 2-3 weeks?"
The answer, I think, is yes.
Starting in 1 week from today, the next 22 games will look like this:
3 @ MIN (63-99 in 2011)
4 @ CHW (79-83 in 2011)
3 v OAK (74-88 in 2011)
3 v BAL (69-93 in 2011)
3 @ KC (71-91 in 2011)
4 v CLE (80-82 in 2011)
2 v SEA (67-95 in 2011)
That gets us through May 15th. That will be 4.5 weeks from Ellsbury's injury, so he will need another 1.5-3.5 weeks to get back. But regardless, Crawford will be back in the middle of that stretch, and our OF will be Crawford, Ross, and Sweeney. That outfield will be able to get it done.
Keep in mind, this team had the best offense in baseball last year, and the RF had a .652 OPS, and the LF had a .723 OPS.
With the additions of Sweeney and Ross, and if Crawford can return to form, the Sox outfield offense as a whole, while not being as good as 2011, could easily get close to being as good as 2011.
All that to say - there are other areas that need improvement more than the OF unless a situation arises where Ellsbury will miss significantly more time than anticipated right now.