Correct me if I’m wrong, I’m not a native German speaker, but “adequate” seems to have more of a negative connotation in the context of the English sentence than “geeignet” would in the German sentence. “Appropriate” or “suitable” seem to be alternate translations of this word that are more commonly used, and that would be a bit more neutral in connotation in English. I would only say “adequate” in English if I meant “This person is technically suitable to the job, and he will suffice, but I would prefer to have someone more qualified.”
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The connotation of geeignet would depend on context, intonation and the speaker himself. In and of itself, geeignet` has no particular connotation, other than being a bit stiff.
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If it doesn’t have much of a connotation, then I think this English translation could be improved.
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I think that “He is suitable for this job.” would be a better and correct translation. 
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