I tried something similar by giving each civ extra settlers in the beginning, but after testing this a few times, they only ever used these settlers as often as they would if they didn't have them right away, so they basically piled up around their capitals and built as few cities as usual.
I guess the rate at which AI settles doesn't depend on settler costs too much but rather stuff like amenities (i.e. they only settle a city if they have the luxuries to) so I'd probably have a look at that.
You could for example just crank up the number of cities all luxuries can be shared to. That should be possible with like one or two lines of SQL, I'll have a look once I'm on my PC again.
There might also be some variable somewhere defining the settle-aggressiveness of AIs but my knowledge of CiVI AI modding is fairly limited
