I think I may have some useful insights, but I'm not sure if it will answer your question.
Sine waves have a period of 2pi, which is an irrational number. Computers can only approximate irrational numbers. Whenever you go to sample your sine wave, you're taking an approximation in the value (because computers don't have infinite precision) and you're taking an approximation in the moment in time of that value. Or perhaps there's only one approximation. That is, you could have a rational time, then you'd require an irrational value for sine. Or you could decide you want a rational value for sine, and then you'd need an irrational value for time.
If you have a waveform of N samples, you can only fill it with complete cycles of a sine wave. That means
waveform = sin(2*PI*i*k/N) where 0<=i<N and k is 1, 2, 3, ...
Your question seems to ask whether non-integer values of k make any sense. I don't believe they do for any fixed size waveform table.