Both poverty and climate issues are extremely important. Neglecting either one of these issues would be terrible. Poverty leads to low income, lower life expectancy, more likely abuse of alcohol, drugs, and tobacco. Climate change is equally important because we are essentially removing the ability for humans to live on this planet. Both issues are important and basically unrelated.
Yes, if the UN prioritized poverty over climate change, climate change would gradually improve on its own. People who are starving and living in poverty do not have the luxury of caring about tomorrow. If poverty decreased, these groups could develop better technologies to tackle climate change, and would also have the luxury and disposable income to meet these problems.
The climate is the most important issue for the UN as this is the only way that is can be completely dealt with, Global warming threatens the entire world and the richest of countries are causing it. Poverty can be dealt with buy individual countries by their respective citizens. The citizens of one country CAN NOT fix climate change, there for we need a coalition of countries to act together with one goal in mind. I do think that poverty is a problem around the world and yes it threatens lives, but it is very clear from a scientific and statistical standpoint that the problem that stands to cause the MOST death is not poverty, but a warming climate, a world where droughts, floods, hurricanes, tornadoes, tsunamis, sea levels rising, mass animal migration, melting poles, both cold weather and warm weather extremes, etc. is what threatens the world and all of its people.