I do think that over-population in under-developed countries is responsible for appalling poverty. And in Senegal, desertification is a big problem due to over grazing by goats etc of what was once savanna, in conjunction with a huge diminution of the annual rainfall (one could say complete failure!) This has caused the Sahara to spread southwards at an alarming rate, and for village wells to become almost dry as the water level falls beyond what a very long rope-and-bucket will reach.
There are large signs put up by the government all over Casamance for example (southern Senegal), warning about not letting goats eat all vegetation in an area. I saw many 'ghost villages'- no well, no people.
The result (in many W African countries I've visited) is a mass migration to the big cities. Once there, the population burgeons, putting a strain on resources (sewage for example, and general pollution with food preparation, encouraging vermin) As health declines, epidemics take hold.
While my husband's family aren't exactly contributing much to global warming, by producing so many children in rather poor health they're making their own lives much more difficult. I have never seen so many rats & cockroaches, and we were all afraid of Ebola, cholera, typhoid, polio, hepatitis and other infectious diseases.
To sum up then, controlling population would improve their lives enormously, slow desertification somewhat but not address climate change in any meaningful way (in my humble opinion).