It would likely depend on who was doing the pronouncing. Mehmet and Muhammed are both the same name after all (محمد), and in the Ottoman context neither reading was necessarily more "correct" than the other. The most common transliteration Ottomanist historians use for محمد is Mehmed. While normally one would be able to look at foreign sources to determine pronunciation, they too were aware that "Mehmet" and "Muhammed" were the same name, and their spellings are thus skewed as a result. In the 17th century, Paul Rycaut calls Mehmed IV "Mahomet," which is just one of the English ways to refer to the Prophet and doesn't necessarily reflect how it was pronounced by the Ottomans.