Born in Genoa, Draghi was a scholar of Domenico Piola, active in Parma and even more in Piacenza.
Draghi was one of the painters who was commissioned canvases for the i Fasti Farnesiano found in the Palazzo Farnese of Piacenza.
The cycles of canvases for the residence depict historical events involving the Farnese family.
Sebastiano Ricci and Domenico Piola were among the other artists in the first series (1685–1687), depicting the history of Alessandro Farnese, were completed for Ranuccio II.
The canvases were taken to Naples by Carlo di Borbone in 1734, and some returned to be exhibited in situ at Piacenza in 1928.