The current is relatively low, just a few amps, and the potential (voltage) is also relatively low at US/CDN/MX 120v.
I taped a run of 14/3 to my FOH snake 28 years ago and never looked back and never had an induction problem, either.
Today we tape our 8/5 FOH AC lines to the drive snakes rather than the input snake as current demands are higher and the noise accumulation across 48+ inputs *might* be an issue. I can't recall it ever happening, though. The input snake and drive snake are usually next to or on top of each other and we've never had a problem.
I'd be hesitant to run mic snakes next to the 4/0 feeder the lampies are using, however.
Have fun, good luck.
Tim Mc