Humans getting periods is the exception, not the rule, considering the majority of mammals do not experience a period. Considering the origins of omegaverse, and that they go into an estrus cycle and not a menstrual cycle they would not have periods. The real question should be "what happens for an omega female?" since they would, in theory, experience both.
I have not. But I also don't see it mentioned too frequently even outside of omegaverse. So, I wouldn't expect to see it brought up at all.
Either way, I think it might be something left up to the creator. In theory animals who experience estrus would only be fertile during their heat as well, but it's common enough in omegaverse for an omega to get pregnant outside of their heat. So that implies at least some overlap of human traits.

Do ya’ll think omega men get periods?