Interestingly, the Ottoman sultans would likely have disliked the AKP. The Ottoman Empire was characterised by building up institutions; even the modern-day Turkish military was a byproduct of the empire's institutionalism, whereas the AKP is the complete opposite.
Also, as a side note, neither Atatürk nor the First World War brought down the empire; it was the Young Turk Revolution that ultimately led to its demise. Atatürk saved what was left of the empire's territory and attempted to establish a replica of the French Republic.
Copying the French Republic was not a good idea, and he should have designed a government that was more fitting for the Turkish people; nevertheless, his actions could never be called a Coup.