The biggest problems is that there is too little Christian contact for a long term conversion to be plausible. There is a lot more contact with Muslims countries, and a lot more benefit to remain Muslim. You don't gain any strong allies by converting because at most there may be a few ships trading every year. You also don't necessarily gain access to the benefits of a more advanced civilization which you would normally get by converting such as a literature culture, advanced technology, and acceptance into an international order. Those achievements were already won.
So while an individual Sultan might indulge on a whim or interest to become Christian, I think there would be much more pressure to convert back to Islam for future generations. Stranger things have happened, but the odds are against it.