Does sitting like a turk reveal anything about humpty dumpty's character?

No but it reveals a lot about the expectations of society when the comment was made or written down. The Ottoman Empire was very powerful and often a threat to Christian Europe right up to the Eighteenth Century. The turks in question were seen as the richest and sometimes the most powerful people in the world. Saying he sat like a turk is saying he was sitting in a relaxed manner.