The problem with Germany deploying an aircraft carrier is, simply, the same problem that Russia, China and to a lesser degree India have run into: operating an air wing is hard, tricky and requires constant practice. The ship you build, thinking you have air operations covered, turns out not to work very well at all... Britain, the US and Japan took decades to work out carrier ops, only to see much of that invalidated when war broke out. The way they operated aircraft in 1945 resembled air ops op 1936, but all the details were worked out, changed or mutated.
If Germany had deployed Graf Zeppelin it would have taken them 8 years to catch up to the Royal Navy.
A far better 'What If' is, what if the German Navy had co-operated/had the co-operation of the Luftwaffe in developing and using naval strike aircraft.
@Sunforged General -
Top tier would be monsters like the Yamato class battleships, or modern battleships with all the bells and whistles like the Iowa class. Bismarck would be mid tier at best, her design was obsolescent and if I'm not mistaken, did not use the more modern, all or nothing armor scheme.
In other words, every modern warship built after the expiration of the building holiday - except Bismarck. Nope, don't buy it.
Bismarck's design was wasteful with tonnage and the Germans spent too much effort on fancy things that didn't work quite right (super-high pressure engines, super-high velocity guns, AA fire control) but there wasn't anything wrong with Bismarck that a year or two of peace and a refit or two wouldn't have solved. I can't say that she had more problems thatn, for example, British AA fire control or a US stern/prop design that limited the North Carolina class to 22 knots. A better, more-experienced design team could have trimmed her down to 38-40k without loss of combat power, but she still ranks comfortably with King George V, North Carolina, Littorio and Richelieu. Pretty much every battleship built after the expiration of the building holiday deserves to be classed as a modern fast battleship and Bismarck falls into that group as do the others you mention.
Btw, no point in saying the Iowas were "modern battleships with all the bells and whistles like the Iowa class". They were equipped the same as the North Carolina and South Dakota classes - same electronics, main and secondary batteries - but if anything were a bit weaker due to their longer, thinner hull; those extra 4-6 knots of speed came at a price. We romanticize the Iowa class because they were the last and largest, not necessarily the best.