Most of this response will draw upon Spanish Society: 1400-1600, written by one of my undergraduate professors, the ineffable Teofilo Ruiz.

The short answer to your question is: probably not.

The Habsburgs might have had a chance, particularly after Charles I inherited the crowns of the Spanish empire and as Castilian cultural, political, and administrative hegemony began in earnest. But as you have likely already noted, the union of Castile with Granada, Navarre, Portugal, and Aragon was superficial at best.

One must emphasize that this unity was only fulfilled in the figure of the king and that the deep political, economic, social, cultural, and linguistic differences of a previous age remained almost unchanged (25).

Moreover, the Habsburgs were much more concerned with European intrigue than they were with integrating the Spanish kingdoms. Spain was constantly embroiled in central European affairs, something that would contribute to the eventual demise of the Spanish Empire under the Hasburgs. Habsburg policies would also open "deep rifts in the social fabric of Spain, brining economic collapse in the mid-sixteenth century and worsening social conditions late in the century and throughout most of the next one" (29).

It is also important to appreciate just how difficult the task of nation-building would have been. Even the Catholic Monarchs understood the impossibility of this endeavor:

1. Geography and climate: from the green Spain of the north; the high, dry plains of Castile; the imposing mountains, rivers, and valleys of the south; and the thoroughly diverse landscapes of the east—nothing about Spain's geography can be considered monolithic. And this is to say nothing of Spain's many and varied subregions.

2. Language: there was no "Spanish" language to speak of. Yes, Castilian would eventually ascend the Galician and Catalan languages, among others, but the latter languages were never entirely dispensed with.

3. Ethnic identity: consider the Basques, who would mount fierce resistance to Castilian centrality even in the absence of linguistic cohesion.

4. Politics: entirely fragmented, "invertebrate."(Ortega y Gasset). The Catholic Monarchs may have centralized authority in Castile, but they would not be able to overcome the power of local traditions and institutions. The Habsburgs may have planted their capital in Madrid, but the Crown of Aragon would continue to pursue its own goals and governances.

As Ruiz explains:

If we think of Spain in the plural—the Spains—it is not only because in 1400 or in 1600 a unified Spain in a true political sense had not yet come into being, but also because the country as a whole (that is, geographical Spain) was, and remains, sharply divided into distinct topographical and climatic regions...Castile may have become synonymous with Spain because of its demographic and political hegemony in the late Middle Ages and early modern period, but Castile was certainly not all of Spain...This kind of 'history from the centre' regards politics as the prime mover of historical events and subordinates the study of social structure to that of political power. Geography teaches us otherwise (11).

My response, of course, does not even begin to scratch the surface of what a more experienced historian could provide.