What arugula to does Thomas Jefferson makes in this excerpt from the Declaration of Independence

Yes, James Madison would define modern corporations as "factions."  He saw factions as groups of people with shared interests (especially financial ones) that group together to gain advantage for themselves over others in society.

Madison's apprehensions about factions focused especially on the role of money and property in creating competing groups in society based on their wealth or property holdings.  Landholders could be such a faction.  Banking and moneylending agencies could be such a faction.  We could add that large modern corporations are factions in the same sense.  They might work their will against the majority of the people.  

Madison argued that factions of any kind war against the unity of the republic.  Factions consider only their own position, rather than the rights and well-being of the whole community or nation.