Definition of a System
Well, yes*, in the same way that all computer programs can be represented as a function of their inputs and time. Hence simulators exist for most kinds of electronics that people build.

The (*) is there because you have to make a number of simplfying assumptions. Real world components have properties that are temperature dependant, and real systems always have a certain level of noise. Most of the time you can approximate this out, but sometimes it matters; you can build a pretty good random number generator by amplifying a noise source.