Although there might have been some such cases, this isn't something I've come across much in literature - where rather the ideological and structural influences of "reconquista" on conquista are usually stressed. A few caveats for your question that made this scenario more unlikely:
a) The major Spanish Christian campaigns against Muslim kingdoms were over by the mid-13th century, with the conquest of Granada starting over 200 years later. The Catholic monarchs' (Ferdinand & Isabella) campaigns against the Granadan Nasrids started in the early 1480s lasting until 1492. On the other hand, the first Spanish campaigns on the Americas' mainlands took off in the 1510s (Cortés in 1519) and more strongly from the 1520s onwards after the fall of the Aztec Triple Alliance. So we can count roughly 40 years between the first campagins against Granada and the beginning of mainland colonisation - leaving aside here the Carribbean colonisation, headed by the Genoese Colón.
b) The most part of the "conquistadors" were neither nobles nor from Castile or Aragon, the centres of the Granadan campaigns. Rather most of these Spanish forces had held lower position back in Iberia, including farmers and bureaucrats. For the Peruvian campaigns, Matthew Restall mentions that "these men were not professional soldiers, but professionals and artisans who had acquired various battle experience and martial skills", often during earlier conquista campaigns. Many of those came from poorer regions like Extremadura and Andalucia, hoping to improve their standing in the Americas. Often leaders like Cortés and Pizarro came from the lower nobility (hidalgos). What is more, "the average age of the men who went to both Peru and Colombia was 27" (Restall again), meaning that most of those participating in these later campaigns in the 1530s were actually born after the conquest of Granada in 1491/2.
So that there seems to be overall a big time gap between the Granadan conquest and American conquest campaigns; as well as well little overlap between occupation, age and origins of conquistadors in Iberia and the Americas. Again, there may well have been cases of overlap, but they would have very probably been in the minority.
On a related note, what we do sometimes find then are rare cases of conquistadors returning from the Americas to fight in Europe. The most famous one is probably Hernan Cortés who took part in a Spanish mission to Northern Africa after his victory over the Aztecs - he had gone to the Spanish court to successfully secure his Mexican holdings (encomienda), but had become quite disillusioned after the drawn-out North African mission.
A later interesting case is that of the "mestizo" Garcilaso de la Vega. A son of an Inca princess and a Spanish conquistador from Peru, he went to live with family in Spain in the 1560s where he would publish to great success a history of Peru (the only published work by any indigenous author during the colonial period). He would also take part in the major Spanish campaign against converted Muslims in Iberia in the 1560s - known as the 2nd war of the Alpujarras. I wanted to mention this esp. to show that while officially the "reconquista" was over in 1492, Muslims continued to live in Iberia until their final expulsion in the early 17th c., although they were forcibly converted to Christianity in the early 16th century.
Overall though, these two are again quite exceptional: for most conquistadors the main goal was to receive an "encomienda" or other recompenses for their parts in the conquest campagins. And although most did not receive the hoped for riches, a return to Spain was complicated, and would have meant a return to a place that many had fled with hopes for "greater destinies". On the other side, Garcilaso de la Vega remains unique in many ways, since not many indigenous or mestizo Americans managed to live and enjoy success in Spain.
As I mention in the beginning there's a difference between the smaller influence of "reconquista" soldiers, and the big influence of Iberian ideals and structures developed during the medieval Christian military campaigns on Spanish America.
The Spanish drew many parallels between (Iberian) Muslims and America's native populations. They perceived the previously unknown lands and their inhabitants in relation to what they knew from Europe. This meant especially applying institutions and negative views of the Muslims developed during the centuries-long Iberian "reconquista" to the new Spanish overseas possessions - in a variety of areas, incl. religion, law, and arts.
Since this moves beyond your question, and since I've written quite a bit about this before on AH I'm adding some of these earlier answers here to hopefully provide a better picture of this longer term influence:
A more general one, talking about literature and arts in colonial Mexico
This one focused on the example of rituals known as cristianos y moros in Spain and central America
As an intro to those I'm adding my conclusion from the 1st answer:
the reconquista and its parallels with the crusades were extended to Ibero-America and transformed as important ideological features of early colonial life ... This intellectual transmission can be seen in literature and art (e.g. with St. James „mataindios“), but also in religious and territorial concepts (like the requerimiento). The transformation of these medieval concepts would continue in New Spain [i.e. colonial Mexico] in different ways with the conquistadors' decreasing influence towards the mid-16th century, and increasing importance of religious orders and gradually of creoles.
Edit: spelling; last part