At sixteen he finished the expected grades and was admitted to the novitiate of the Society of Jesus in Trencsén, Hungary (now Trenčín, Slovakia), where he stayed for two years.

Later he studied philosophy in Graz, Austria and in 1725–1726 he lectured on the elements of grammar at the Jesuit Academy in Zagreb in Croatia.

During his expeditions, Consag recorded information on the peninsula's unknown topography, natural resources, and native inhabitants.

Alexander von Humboldt used the maps in his work Carte generale ... de la Nouvelle Espagne, (Paris, 1804).

His diaries, after his death translated and reprinted into many languages, were published during his lifetime by Villa-Señor y Sanchez, Ortega-Balthasar, and Venegas-Buriel.

There is an outcrop in the northern Gulf of California named Roca Consag, located offshore near San Felipe.