I don't think so. His father, the Duke of Anjou and Cadiz, was a Spanish HRH under Franco's 1972 decree. The royal decree of 1987 confirmed that title/style, but explicitly barred it from being transmitted to the Duke's offspring, including Luis Alfonso, who was never a Spanish HRH in his own right.
My interpretation is that D. Luis Alfonso is an Excelentísimo Señor though because his mother is a duchess and grandee of Spain and heirs to a grandeeship are entitled to the style of Excellency.
Well, not only his father, but his descendents, were Royal Highnesses by the 1972 decree, and were recognized as RH.
The Duke of Anjou's brother, François/Francisco was buried in Las Descalzas Reales as HRH.
This is why, the Duke of Anjou being already RH before the 1987 decree, should be treated accordingly (but not his wife or children).
As to renunciations, Spain is quite legalist following Castilla (while Aragon was prone to usurpations) and a dynast person can cease to be so, only by Royal decree PLUS vote of Las Cortes.
Las Cortes, culturally, tend to accept renunciations where there is really a marriage that is "notable y manifiestamente desigual" or other "very serious" motive, but are quite reluctant to accept any renunciation which may deprive a next of kin succession; both because in Spanish mind, close relation between a King and his successor are more important than elsewhere (to the point of preferring a second son to the children of a predeceased elder son, until the publication of the Ley de Partidas), and because in 1699, Spain would have been without close successor, had Infanta Maria Teresa's renunciation been voted when she married Louis XIV of France. Fortunately it had not been voted, and her grandson Philipp could reign.
I am speaking here only of succession law, not of right to titles. Titles, honours etc depend on the sole King's will and for instance, the Pragmática of Charles III deprives princes in case of unauthorized marriage, as well as marriage considered unequal, of their titles, honours etc unless stated otherwise. But the Pragmática is private/civil laws, non related to succession otherwise than by diminishing the political weight of a Royal reduced to mere nobility at the Court, which was the purpose of the Pragmática (a younger brother of Charles III being used by Court intrigues as a threat against him; when
this younger brother became mere Earl of Chinchón, while not excluded from succession, nobody at Court tried anymore to settle him as King instead of Charles III).
It seems clear that Alfonso XIII didn't wish to oust Infante Jaime (nearly deaf and mute) before the Prince of Asturias' unauthorized marriage with a plebeyan. He was supposed to remain a younger son, later uncle and excluding him was deemed unnecessary. But when, after Alfonso XIII's exile, his elder son did this marriage, he sent a renunciation, and Alfonso XIII managed to extort a renunciation from his second son Infante Jaime (later Henri VI in France), and later married him to the daughter of a Duke and a Princess of a formerly semi-sovereign house.
I have always felt that Alfonso XIII had no doubt as to his coming back to reign. He would have, then, asked the Cortes a validation of the renunciation of these two princes. Whether he would have succeeded to get such votes is unknown. Based on case law from XIXth Century, he may well have succeeded as to his elder son, Alfonso. I don't know if he would have succeeded with the second (based on his handicap) before the birth of this prince's first son, but I am quite sure he would not have succeeded after the birth of his sons, his handicaps becoming only a transient thing. By no way Infante Jaime may have been excluded on the only motive of his unequal marriage, there are various examples of Spanish Royals retaining their succession rights in spite of a marriage in the nobility — provided the marriage was authorized, and Infante Jaime's was.
But it happened that Alfonso XIII did not succeed in coming back to the throne. His elder son died childless before him, so his second son succeeded to his legitimate claims, not his third.
But present day monarchy is not the old one continued. It is a monarchy instituted in 1947 with Franco as head of State, this having to be succeeded by a King to be chosen among several princes. When Juan Carlos was chosen in 1969, this choice didn't imply any exclusion of other Royals, either in the traditional succession, or in the new monarchy.
