Of course it is. In general, Enlightenment period was fascinated by the Roman (and Greek) political philosophy, architecture (look at columns and white marble at Washington DC), and social structure (justification of slavery).

Eagle grasping a thunderbolt was a symbol of Legions and of Jupiter in Roman times. As such, it appeared after much deliberation, on American Great Seal, with a Latin quote (from a recipe for cheese sauce). It is not true that Franklin wanted turkey to be America's national bird (though he jokingly criticized eagles and praised turkeys in a letter to his daughter) , but other designs included a phoenix, for instance.