Benefits of oversampling in a realtime noise-cancellation system
The system has zero time delay (sampling, calculations, etc. are instantaneous)


This is an invalid assumption. Almost every digital system has at least one sample delay. DAC and ADC or clocked off the same master clock. So at sample time n, the ADC is acquiring sample n while at the same time the DAC is outputting sample n-1. The only way around this is using a much higher master clock, donwsampling that clock and clocking the A/D and D/A on different phases. However that's equivalent to running at a higher sample rate in the first place.

So your ability to cancel is given by how much the amplitude of the sine wave changes during 1 sample. The residual signal is simply given by $$e(t) = \sin(f_0 \cdot t) - \sin(f_0 \cdot (t-T_s)) = 2 \cdot \cos(f_0 \cdot (t- T_s/2)) \cdot \sin(f_0 \cdot T_s/2)$$
 where $T_s = 1/f_s$ is the sample time. The error is simply a function of the ratio of signal frequency and sample rate. For $f_0 &lt;&lt; f_s$ the error is very small.

The only way to get around this is to crank up the sample rate or use some a priori knowledge of the signal to do some prediction and speculative cancellation.