A bleached anemone does not possess any zooxanthellae from which it would otherwise harvest energy. Without any additions of food they can starve to death just like anything else. A healthy anemone with all of its own zooxanthellae is basically self sufficient and as you've demonstrated does not need supplemental feeding. But thats not to say that it wouldn't benefit from a few scraps on occasion. Anemones are pretty good at capturing food on their own too. Or if you have clownfish with them they will probably feed it for you.
The anemone in the picture is looking a lot better. Previously when it had its insides coming out from its mouth it looked like many of the dead ones I've seen at our LFS.
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