Short answer:

Generally, no. These events take place in different contexts, socially, politically, religiously and technologically, over different periods of time. So while the history of Spain contains echoes of its past, in this case looking for parallels will tend to obscure more than it explains, the Reconquista and the Spanish conquest of the Americas need to be understood as distinct historical processes.

Discussion:

Start with the word that the Spanish use for what you term the "conquest of the Iberian Peninsula"-- its not "conquista" its "Reconquista" = "the Reconquest". There's a big difference between a "conquistador" and a "reconquistador" (the latter term is rarely encountered). This is fundamentally a medieval project which extends into the earliest part of the early modern era, and it's the vindication of an ancient grudge, taking centuries rather than a gold rush, that happens very quickly. The Spanish conquest of the Americas is much more distinctly of a modern nation, it's more avaricious military entrepreneurs and its raison d'etat.

Ibn Khaldun summarized what Spain meant to the Islamic world:

From the time that Spain was conquered by the Muslims, that land beyond the sea has always been a frontier of their empire, the setting for their holy wars, the field of martyrdom, and the gateway to eternal happiness for their soldiers. Muslim institutions in that country were constantly on a flaming brazier, so to speak, placed as they were between the claws and fangs of the lions of infidelity. Surrounded by a mass of hostile people, the true believers of Spain still find themselves separated from their coreligionists by the sea

That Muslim perception mirrors at least in part the Christian understanding-- that Muslim Spain was a beachhead "beyond the Sea" (meaning the Straights of Gibraltar) into Christendom, a challenge which potentially threatened all of Christendom with a competing religion and world historical vision which had similar competencies and posed an existential military threat. Neither Spaniards nor indigenous peoples of the Americas perceived the indigenous peoples of the Americas in any similar light.

The mission of the Spanish Catholic kingdoms in their fight against "the Moors" (a frequently encountered but unhelpful term-- we're speaking of plenty of Arabs and Spaniards) is an irredentist one, a reclaiming of land for its rightful owners; a repulsion of invaders, and and retrieval of lands for Christendom which had previously been Christian. All of these dynamics implicate different behaviors than in the New World, a place with no previous European sovereignty, no previous Christian religion. The New World is, for Europeans, like landing on Mars, from the point of view of the law a terra nullius, until European powers reach some agreements by war or negotiation (as at the Treaty of Tordesillas). Spain had long and complex diplomacy with the Muslim kingdoms, periods of war and peace, truces arrived at and generally observed, trade relationships. Spain's relationship with indigenous American polities shares little-- Pizarro's treatment of Atahualpa resembles Cortes' treatment of Moctezuma, but it's quite a different category of cultural encounter to Christians and Muslims in Spain. Christians in Spain had, after all, had the experience of centuries of Muslim rule-- these were competitors and heretics, but a very different category of culture from the European/indigenous interaction.

The relationships between the Christian Spaniards and their enemies in Spain were very different from the relationship of the Conquistadors with indigenous peoples. Consider the complex politics of the Taifa Kingdoms, where Christian mercenaries, like the celebrated "El Cid" (Rodrigo Diaz de Vivar) who served both Christian and Muslim Kings. While Islam may have been a political adversary, as a world civilization it was understood to be a source of knowledge-- all kinds of works, particularly of medicine and science-- were translated from Arabic to European languages in Spain, creating a very different view of the adversary. And the international politics are different as well-- where France, England, Portugal and Spain compete in the New World, there is far more cooperation in the Reconquista; indeed one finds English Armies allied with Castile at the siege of Algeciras, very generally this long campaign is considered a kind of crusade

Finally, the status of the conquered kingdoms of Spain upon the completion of the Reconquista was very different. Conversion to Christianity was ultimately necessary, but for many years the mudéjars -- Muslims who had sworn loyalty to the Christian kingdoms-- were tolerated as such. The Spanish built over the Aztec capital of Tenochtitlan, but Umayyad mosques and palaces remained pretty much as they were-- religiously repurposed, but very much extant. So the Great Mosque of Cordoba becomes the Cathedral of Our Lady of the Assumption-- with much of the original architecture retained. So there's a very large Muslim jurisprudential effort to clarify how a Muslim living in Christian Spain ought to behave-- there's no similar tolerance for Inca or Aztec polities, no equivalent to the mudéjar.

Sources:

The Legacy of Muslim Spain

BARTON, SIMON. “‘El Cid, Cluny and the Medieval Spanish’ Reconquista.” The English Historical Review, vol. 126, no. 520, 2011, pp. 517–543. JSTOR, www.jstor.org/stable/41238713.

The History of the Conquest of New Spain, Bernal Diaz del Castillo

O'Callaghan, Joseph F. The Gibraltar Crusade ( University of Pennsylvania Press: 2011 )

Peters & Reinhard eds. Islamic Law and the Crisis of the Reconquista ( Leiden: 2015 )