No, they aren't.
Let's look at that wikipedia entry on
"continuous functions" as you suggested and see what it says:
"In mathematics, a continuous function is a function for which,
intuitively, "small" changes in the input result in "small"
changes in the output."
The output of the comparator circuit (what you call the
"modulation duty cycle") defies this description. There is
a threshold on the input that results in a large jump (a step
function) on the output.
The modulation duty cycle is defined as the percentage of time that the output is in one state as opposed to the other. It is a continuous function of the input voltage. The duty cycle, not the instantaneous state of the output devices, is the analogue of the input voltage.
The charge on any node of a circuit is a discrete number of electrons. Does that make any circuit digital? And if you hook up a high speed scope to any digital circuit, you will see continuous waveforms. Does that make all digital circuits analog? Again, look at the properties of digital circuits in the Wikipedia article. The distinguishing features of digital circuits have to do with what the signals represent and the way that information is propagated. For instance a digital circuit has unambiguous rules for what makes a transition from 0 to 1, and the circuits are designed to enforce these rules.
By the way, I am taking this all in the spirit of friendly discussion, and it isn't really a big deal anyway. If we understand how a switchmode amplifier works in detail, then it doesn't matter what we call it.