Are multiple reflections accounted for in S-parameters?
Is it correct to say that all these waves reflected back into the generator are summed up and therefore accounted for in the calculation/measurement of S11?

Yes.
That's part of the beauty of S-parameters.
Perhaps it might help you believe that it works, and isn't magic, if we review what happens when you take two of these 2-port things you've just measured, and cascade them, with or without an intervening 50 ohm line.
Cascading involves use of Mason's Non-Touching Loops rule, aka Mason's Gain Formula to combine them. As well as a simple product of the S21s in the numerator that you'd expect, there's a tricky 1+/-loop_gains in the denominator that handles these multiple reflections.
If you do cascade the 2-ports via a piece of 50 ohm line, then you are cascading three sections, and although the middle one is 50 ohms so S11=S22=0, it's vital you include its electrical length in the phase of S21 and S12, so that the reflections add up correctly.