Or was the plan always for them to be simply strong and close allies in European affairs?
Only under the reign of Charles V were these domains governed under a single executive head. It was not a single political entity; kingship (and by extension empire) in the early modern period tended to be what are called composite monarchies. A composite monarchy means that central ruler directed state policy, but recognized the unique local conditions and customs and had to pay due deference to regional elites. Thus Charles V was not "King of Spain," but King of Castile and León and King of Aragon and Sicily, and Count of Barcelona and known as Charles I in Spain. The unique conditions that brought Charles V this vast patrimony (the right level of marriages and timely deaths of heirs like John, Prince of Asturias) and encouraged some political thinkers to float the idea of a universal monarchy under the aegis of the Hapsburgs. The Florentine historian Guicciardini wrote that:
the foundations of the greatness of Charles were such and so mighty that adding that dignity imperial, there was great hope that he might reduce into one monarch all Italy and a great part of Christendom.
But although the spirit was willing, the flesh was weak. The nature of this composite empire meant cracks showed as soon as Charles V flexed his muscles. The local elites often perceived their monarch as pursuing foreign interests rather than native ones; an imperial mentality never really coalesced within these leadership bodies. So Castilian elites saw little reason for their taxes to go towards Charles's Italian and German wars, similarly, Burgundian bodies did not like sending wealth to fight the Turks. The tenuous nature of communications in the early modern period precluded any timely smashing or mollifying of dissent. The latter period of Charles V's reign was spent putting out the fires of these revolts. Meanwhile, organized Protestantism's arrival added a further religious dimension that ate away at the cohesion of the empire.
So when Charles V abdicated, he hoped that the Hapsburg family (his son in Spain, Italy, and the Netherlands, his brother in Austria) would work in synchronicity. This split reflected how much he had been overwhelmed in the last decade of his reign by various crises. His 1548 testament to his son, Philip II, instructed him to visit his various domains and build personal relationships with regional elites. In the subsequent century, Spain and Austria tried to have a degree of a unified foreign policy, but were often at odds with what direction that policy should take. Spain wanted imperial help to crush the rebels in the Dutch Republic, but such aid against this bastion of Protestantism would upset the delicate confessional balance in Germany established by the Peace of Augsburg.
Sources
Maltby, William S. The Reign of Charles V. New York: Palgrave, 2002.
Tracy, James D. Emperor Charles V, Impresario of War: Campaign Strategy, International Finance, and Domestic Politics. Cambridge [u.a.]: Cambridge Univ. Press, 2002.