Graf Zeppelin's real danger in a surface task group

Did the Kriegsmarine genuinely want Graf Zeppelin, and how dangerous would she have been?

Yes; she was questionable alone but potentially dangerous as the scouting arm of a capital-ship raiding group, whose broader weakness was inadequate light-cruiser support.

The Kriegsmarine did want a carrier and understood that aviation could locate convoys and protect raiders from British hunting groups. A British assessment estimated that carrier reconnaissance could search about 20,000 square miles in a day, find convoys, screen raiders from hunting groups, and extend attacks towards the Western Approaches. Graf Zeppelin operating alone would have been vulnerable, but paired with Bismarck or the Scharnhorst class she could have made a commerce-raiding group much harder to find and intercept. Germany's shortage of capable light cruisers remained a major weakness in assembling balanced task forces.