Imperialists? Weren't the kings of Castille, France, Aragon, England etc. all imperialists. I think you mean the HRE?
Sorry for any confusion. There was only one emperor - the Holy Roman Emperor. All the rest were kings, and it follows from that there can be only one bunch of imperialists in this case - those that support the emperor.
Is this acceptable to the Holy Father? IIRC, there was a lot of bad blood between Giovanni Sforza, the tyrant of Pesaro and Cesare Borgia, son of Pope Alexander. Does this mean that the Pope will be on the side of the Castilian-Burgundian alliance?It depends on the POD, but a duchy of Milan under the Sforza dukes might be the most acceptable compromise. However things change when the line of Sforza dukes goes extinct.
Hmmm - I see. You think it is unlikely that a French domination of Milan is unlikely? Is it impossible for the French to repeat their Italian conquest - I mean - a la what happened under King Charles with his attempted conquest of Italy, except with a permanent French presence in Milan and a French choice ruler in Savoy?Whether Milan will be French or Habsburg, it might end up in the hands of a cadet branch and with the further arrangement, that the bone who receives the duchy probably marries someone from the other house.
No doubt the relations between Aragon and France would be mired in suspicion, even when they are allied. However, there is one factor you should keep in mind, at least in the first few years of the alliance (well, as long as Ferdinand is alive). Ferdinand was truly humiliated by Philip of Habsburg and the Castilian nobles when he tried to intervene on the side of his daughter, Joanna, which was one reason why he went to the French for his alliance. There was a genuine fear in Aragon that they would become the next Leon - essentially a province of the Castilian empire, with Castilian domination in their own land, which is why Ferdinand tried to split the two thrones. Further, if the Aragonese were split from the Castilians, they might press, more forcefully, their claims on the coast of Navarre and also in the south, on Murcia and the adjoining areas.The relations between Castille and Aragon will be interesting too. OTOH even with Aragon separate from Castille, they still equally dislike a too powerful France or Burgundy-Castille in northern Italy. None the less without the union of Castille and Aragon ITTL logistically it has become more complicated. However don't forget that the Austrian hereditary lands are nearby (the north eastern tip of the duchy of Milan borders the south western tip of the county of Tyrol).
As for Milan, while Austrians are certainly close by, I am not sure that Austria, at this point, was strong enough to challenge France on her own, without any significant Castilian intervention.
As you say, the Austrians and the Castilians have more resources for their war on the Ottomans, particularly on land. But they also would have a greater fear of the French ITTL. So, it is quite conceivable that they might encourage the Ottoman naval exploits, and urge them to go across the straits of Otranto into the Aragonese possessions in Italy. This means that it is the Venetians who are allied with the French and the Aragonese in opposing the naval expeditions of the Ottomans. And the Aragonese are going to need the French help. However, they would encourage the Ottoman land exploits, urging the Ottomans to go after Hungary and other possessions in central Europe. However, all this is predicated on one thing - the French and the Habsburgs cannot come to some accommodation. If they do (Franco-Aragonese domination in Italy in exchange for Imperial domination in the low countries), it is the Ottomans that would be the losers, since both on land and sea, they would be facing greater opposition, and greater forces arrayed against them.I'm not so convinced of a very hostile Aragon towards Castille as long as they don't interfere too much in their respective spheres of influence.
Less involvement in Italy might free up more troops for any conflict with the Ottomans and the protection of their current possessions. A French focus on Italy might be good thing for the Burgundian possessions of the Habsburgs; and furthermore this will result in tensions between the allies France and Aragon. ITTL the Habsburgs will stay interested in an alliance with England (even IOTL with their religious differences, alliances were made, when politics demanded it).
However just as with Ferdinand having a son with his second wife, Ladislaus II of Hungary-Bohemia only had a son (Louis, 1506) and a duaghter (Anna, 1503)with his third wife at a relatively high age. With this POD they would be already born. The Habsburgs might still inherit those kingdoms, which would increase their involvement. And if they do, they might have more means than IOTL in their conflicts against the Ottomans.