Not quite. Napoleon was no great friend of Thomas-Alexandre Dumas, but that only extended to ignoring him when he was imprisoned in Naples and later, when he was back in France and destitute.

Alexandre's flight from France was decades after Napoleon's fall. It was likely mostly to escape his creditors (he was not good with money). Also, his long-time patron, Louis-Philippe, the last king of the French, had just been deposed, and the first elected president of the republic, Napoleon's nephew, did not like Dumas much.