Alternate-history: Catholic Ottomans

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From the book Mehmed the Conquerer and His Times:
>Soon after the terrible news from the Levant, Pope Pius II conceived the strange idea of trying to convert the sultan.
>>An insignificant trifle can make you the greatest, the most powerful, the most famous of living mortals. You ask what it is? It is not hard to find; there is no need to go far in search of it. It can be found everywhere: a little water with which to be baptized, to be converted to Christianity, and to accept the faith of the Gospel.
Once you have done this there will be no prince on the whole earth to outdo you in fame or equal you in power. We shall appoint you the emperor of the Greeks and the Orient... All Christians will honor you and make you the arbiter of their quarrels... Many will submit to you voluntarily, appear before your judgement seat, and pay taxes to you. It will be given to you to quell tyrants, to support the good and combat the wicked. And the Roman Church will not oppose you... The first spiritual chair [the Pope] will embrace you in the same love as other kings, and all the more so accordingly as your position is higher. Under these conditions you can easily, without war or bloodshed, acquire many kingdoms...
We [the Papacy] shall never lend aid to your enemies, but on the contrary call on your arm against those who sometimes usurp the rights of the Roman Church and raise their horns against their own mother.

What would've happaned on the off-chance that the sultan had converted to catholicism.