Absolutely, as in the Zed-Plan.
At the start of the century German industry shocked the world at how many and how fast it could build major warships, even more efficiently than America.
You don't say when to start building these carriers, but it was definately possible. Because Hitler wasn't confident of his support, even after the Fall of France, he kept demobilizing his industries, he didn't even go to full mobilization against either Poland nor France. But if he had, or if they started on a naval program Adm Raeder had been pushing for since the 20s after seeing British and visiting Japanese carriers, definately.
As for planes, they could have developed if they had the Will. There were options made for Me109s, or better yet the He100 or even 112, the Fw190(even with torpedo), Ju87 and He/Bv155. Even some Italian planes were considered. The Germans were not as close to the Japanese as one might think, but if they were and got their help in the 30s working on a carrier fleet, that would be interesting. Not only ships but plane licenses?

Even if at full mobilization, it means less Uboats than could be produced. Whether a surface fleet or submerged fleet is more likely to bring Britain to her knees is interesting.
The British, though inventors and with the largest number at war start, had terrible cooperation between RN and RAF, that's why such disparity between Army and Carrier plane types.

7 Graf Zeppelins even half Seydlitz's or converted Europa's(passenger liners) in 1939? England and France would be in serious trouble.