No Borg please, leave that to Picard where two of the characters have direct, and somewhat shared, connections to them so it makes sense.
There's no reason for the Borg to show up in Discovery's storyline. Besides, the way the Borg are presented in the 24thC, they will likely have reached a point long before the 31st where they either assimilate basically everything and become the dominant power, or are incapacitated/destroyed. Given that we know the first doesn't seem to have happened, I'd guess they aren't around the Galaxy as much anymore. Maybe someone with fewer morals decided to use Data's Borg destroying spirograph.
But we see in Lower Decks (and Star Trek Online) that they are around in the future and surprisingly chill.