Not really, no. It's not so much that overpopulation is a cause of climate change, but it's a major barrier towards finding any real solutions.
I'm not sure that comparing a family of 10 in Somalia with a family of 3 in America is particularly useful here. I can see what you're getting at, but it doesn't tell the whole story. The family in America may be energy hogs and excessive users of fossil fuels and other vital resources. This is true. However, the current trends around the world are towards modernization, development - so that all countries can benefit from living in a modern, industrialized, technologically advanced society.
The family in Somalia may not be contributing as much CO2 emissions now, but over time, they will want to have more - and honestly, who can blame them?
A while back, I posted an article about the burgeoning middle class in India who can now afford and seek to buy such luxuries as air conditioning. Air conditioning is nice to have, particularly in the hotter climates - but there's a tradeoff due to high energy usage and damaging emissions. There are billions in this world, and it's normal that they would want the same things we have enjoyed for decades: air conditioning, cars, superhighways, shopping malls, cellphones, computers, etc.