Yes, Elio and his siblings did go to school before going on their respective journeys and career paths. Typically, they were all A+ students - but Elio was the best and most talented among them; they all graduated early by 16, which is when Elio started his journey around Unova (estimated, to be two years prior to the events of BW).

Since the academy that Elio went to was akin to a university, while majoring in the basics of Contest and Trainer Battles, he also majored in business and investments - which became critical in further building his finances for his personal journey and inevitable emancipation from his grandfather (in a good way!). Typically, he also minored in medicine due to his family business being centrally focused in the medical field in lieu of them running a conglomerate. They're required to have a certain level of medical skills per the dictation of Ardyn.