Very gray area here. In the most traditional sense of the job, a sound effects editor is expected to take sounds that have been selected for him/her by the supervising sound edtior and edit them against the picture. That's it. Anything else and you're not really talking about a sound effects editor anymore.
What sound effects editors are expected to do these days is quite different from what it used to be; it's really an amalgamation of all the disciplines, from recording sounds to designing new sounds to basic and advanced mixing. This requires knowledge of and experience with microphones, recording techniques, librarian skills, sound editorial, sound synthesis and sampling, reverb and EQ techniques, mixing and mastering.
This is the case with both big budget and independent films, in my experience.