Most of the hits on Illustrious were outside the armored area, including a couple which went down the elevator well. The one which did hit the armored section of the flight deck penetrated it and exploded inside the hangar, so the enclosed hangar magnified the effect. US experts examining the ship while she was under repair considered than an Essex class carrier would have survived the same hits just as well, which seems reasonable since the armored deck does not appear to have stopped anything. Incidentally Illustrious never fully recovered from the damage and was no longer able to make her designed speed.
Getting back to the Germans, a small carrier wouldn't be any faster or less detectable than the Graf Zeppelin type, and it might be just as well for a ship operating in the open ocean, far from home bases, to have a reasonably sized air group.
Prior to the Bismarck operation, most German ships were able to get out into the Atlantic and home again all right, so presumably carriers could also. This became progressively more difficult with the advent of radar and long-range patrol aircraft; by February 1942 (the Channel Dash) the Kriegsmarine gave up on operating heavy ships in the Atlantic. Meanwhile, Bismarck and Graf Spee illustrate the dangers raiders faced if anything did go wrong.
A carrier could search a wide area for potential targets or threats, but sighting carrier-based aircraft would also give the enemy a rough idea of her position.
Much might depend on British construction of additional carriers in response to the German program. Germany was not Britain's only concern; the RN would still want some number of modern battleships. On the other hand, a significant German carrier fleet was a clear threat to Britain and not much use in fighting her continental rivals.
The Allies did not start using escort carriers to protect convoys until 1943, so there would be little need for German carriers to counter them. Carriers might provide useful support to the U-boats anyway, although it would take time to work out effective tactics (another argument for a training carrier early in the naval expansion process). Although the Germans couldn't know it, radio communications between carrier, aircraft, and submarine would expose them to Ultra and HF/DF.