Project VAG: Using Arduino Due for current control

I see a problem with the calculated sine wave following the guide

In the code, they use

delayMicroseconds(sample);  // Hold the sample value for the sample time

As far as I understand, the code delays for a minimal amount of time the hold the voltage level. Wouldn't this be a problem when I have to check the primary current for zero-crossings? I mean:
set voltage -> wait for 1 ms -> set new voltage
and in the meantime a zero-crossing occurs, will the code detect it?