A former colleague of mine is an LCSW that did primarily ED work (both in-patient and in private practice), so it is definitely possible, though you'll need to seek out very specific training/supervision to do it right.
I'm not as well versed with SW programs (hopefully pingouin will stop by with her 2 cents), though I do know that they will all have a different split between "Applied" and "Administrative" training. Obviously you'd want to be more on the "Applied" side, though some administrative training would be helpful too.
As for ED specific work....I'd *strongly* recommend getting solid generalist training, working with a range of populations and Dxs, and then later going into EDs under the supervision of someone who specializes in the area. This is my primary population (both clinically and for my research), and I've found that a strong generalist training is needed because there are many layers you will have to deal with in addition to the ED Sx's. Being comfortable working with substance abuse, family dynamics, PTSD, anxiety Dxs, MDD, etc. Also, it is a very difficult population to work with, so you'll need to be grounded in your theory and clinical skills because they will be tested early and often. Being well versed in the literature is really important, because most professionals do not have a good handle on EDs, and they often get referred out because of this knowledge gap.
It can be very rewarding work, but I think it is one of the hardest specialty populations to work with because of the co-morbidity issues, as well as the pervasiveness and longevity of most ED Sx's.