I like the idea of "defections." I don't know if I'd make it independent of culture, though.
I see Overseer714's point about culture not being overly strong in the early game when people are landgrabbing but I think that's a feature rather than a bug; it adjusts the balance of factors so that there is a strategic point to generating lots of culture early, there would be the option of expanding to the borders fast and filling in later, and taking the risk that AI settler pairs might or night not get through to your unclaimed land.
What I probably would do is limit it to land units. I think of it this way: Land units can reasonably be thought of as coming into contact with local villagers and they might decide to settle down, get married & have kids. Ships, on the other hand, won't have the same kind of contact. Their crews will only meet locals if they enter a port & in Civ 3, ships can't enter foreign towns. I guess you could argue that if they end their turn on a sea tile, they're effectively docked, but you could just as easily argue that they're not.
That makes sense.
I also wonder if the settler should change to workers, or simply defect.
It would, I think, be most interesting if it were up to the player to whom they are defecting; granted an AI capable of making a reasonably sensible decision on that.
OTOH, I don't know if there's any way, in terms of programming, to tie the units in the settler pair together. Obviously, if the settler converts but not the spearman, there's a problem, as they're on the same tile.
I had been envisioning that they would either both convert or neither; options for dealing well with only one converting aren't coming to my mind right now.