Why not? It had the range with a fuel ship with it, and the other German surface ships and sortied in mid-1941 in the Atlantic and survived while the USN was looking for enemy ships to report on. The Uboats sent were primarily surface vessels and they got there safe in February.
1. As usual, if it's build what isn't? If we stick to navy then it's less ships, eaning RN has it easier from start. It means KM is weaker and RN relatively stronger. This brings its own set of butterflies so things that were touch and go can be touch instead of go, Norway being prime example. If it's less u boats then RN is feeling less pressure on convoys so they can use more ships elsewhere.
2. It would be prime target for RN once hostilities break out.
3. KM will have to write and learn the book about carrier operations in space of few years. That's operating it as a ship, operating it as a weapon, naval aviation, whole works. Given how "navla" aviation was treated it would be problematic.
4. If it breaks out RN will throw everything and a kitchen sink at it. And carrier can't exactlly hide, like u boat can.