Here is a different point of vue, less global and more city per city :
Assumption 1 : You discover a tech of the current era every ~10 turns (standard speed)
Assumption 2 : The penalty for new cities is 10%
Assumption 3 : We are in Rennaissance Era (works with every era, but numbers are differents)
First half of Rennaissance, techs have a base cost of 1000.
Every additionnal city increase the cost by 100.
Since you discover a city every 10 turns, annexing a city has to increase your production by 10 to pay itself.
Since a puppet produce 60% of an annexed, it means '0.4 x N = 10' so 'N = 25'
So any city producing more than 25 science will speed up your science when annexed. Cities producing less will slow you down unless you invest heavily on their infrastructure.
Second half of Rennaissance, techs have a base cost of 1500, which leed to puppet cities need to produce at least 37 science to be interesting to annex.
Since puppet cities usually have a bad infrastructure, this cap will not be passed. But if you capture a city of an oppopent you are influencial on, since you keep all the infrastructure, it will be interesting to annex this city.