We won't see anything like the Seanchan in the show. My guess is that we won't see them at all, but more strongly it seems that there's no way a 'woke' production could have the good guys team up with an empire of slaveowners to defeat the Dark One's armies, particularly with the resolution that the slaveowners get rewarded with dominion over half the known world.

Based on the trailers, it looks like what we'll get instead is a more powerful and competent faction of Whitecloaks that's a threat to The Dragon and the White Tower through other means. Maybe Pedron Niall's plans of uniting the nations against The Dragon works out better in the TV version or something.