Well, in the intro of the game, we see the Nautiloid (the illithid ship) capturing people in the streets of Baldurs gate. So it makes a lot of sense that many people came from baldurs gate. That part is covered. Karlach is more of a stretch. But considering that all that happens starts with Gortach (even if later his plan was used by the brain), it seems that it is not a coincidence, but a design on his part. And later another oportunists jumps on it.
But yes, Illithids tadpoling everyone is kind of the point. Because it is not just the companions, but also plenty of NPC that cross your path.
