Um, no they're not linked. And yes it's possible to have one and not the other. There are several different types of anemia. Or it would probably be more accurate to say there are several different causes of anemia. And CFS is not one of them.
What they DO have in common, is fatigue. But with anemia, if the anemia is successfully treated, the fatigue will be cured. In CFS, the fatigue almost never goes away, even with what little treatments are available.
I hope this info is helpful. Welcome to the CFS forum, by the way! And please feel free to ask further questions, if you have any, or reply to other messages, if you feel inclined. We're glad to meet you. All best.
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Chronic Fatigue Syndrome forums