If you're going to send the serial data using busy loops, there's no advantage in putting it in an ISR; just leave it as a blocking function called from the main loop. Then the interrupt is disabled in only ~1ms chunks. But if you're doing this, then there's no need to use interrupts at all; just process everything in the main loop.
Anyway, because the requirement is so basic, there's plenty of approaches that will give similar results; the one I posted before doesn't have any need to disable interrupts, and never has to worry about missing a PWM cycle.