Specifically, did the experience of the Great War in Europe - or, even more specifically, of Brazil’s entry into it - play a key role in the rise of tenentismo (or the tenentes, the lieutenants, etc), their activism in the 1920’s, and eventually the Brazilian Revolution of 1930?
It played a role, yes, but there were other factors as important or more in play. Brazil tried to professionalize its military officer curriculum in the first decade of the 20th century, sending three whole classes of the Army military academy to Germany. After WWI, the government tried to modernize the military forces with French(Army) and US(Navy) help. These changes(not limited to military doctrine), and the fact the French were in this mainly to sell surplus equipment, not to teach Brazilian officers how to conduct modern warfare, ironically made those apolitical German-trained officers gradually begin to turn to politics in order to overturn them. Another big factor were slow promotions of Army officers - a lot of officers were spending 10-15 years or more as lieutenants due to a lack of billets for higher officers, meaning those officers with families were forced to make do with a lieutenant's pay. Adding to that, the military academies were some of the most prestigious academies available for the common citizen, with the luxury of selecting the best of a large nation-wide pool of candidates, and so, their alumni were regarded as an intellectual elite. Given that patriotism is an integral part of military education, many officers felt they had a duty to make Brazil a better place.
As for the economy, the WWI years were bad for the coffee planters(which brought in most of the government revenue), but also brought in an industrial surge, as many products couldn't be imported anymore. The increased industrial workforce would also play a role in the chaos of the 1920's. As for coffee exports, those had recovered by 1919-20. The economic downturn of late 1922 would have more of an effect in the rise of the lieutenants than the WWI one.