the lusignan in cyprus disagree with you, they were for almost 300 years in control of cyprus which was a totally orthodox island, but at no time did they convert to orthodoxy, or to bizantine catholicism, I doubt any crusader king would do that., this would certainly be frowned upon by the pope, and also by other nobles in Europe, which could be a problem depending on which house is the king of egypt, not only that, But the conversion could be used by a nobleman to overthrow the king and seize the throne, especially if the papacy does not approve (something similar to the situation of Pedro I in Castile)
It's not impossible, but it would be very difficult to happen,