It probably depends on the politician and on whether s/he has studied up the politics of any particular country. It is possible for anyone to have a solid understanding of anything; but they need to know how to learn about it, and they need to learn both from experts and from the people dealing with situations on a day-to-day basis.
Depending on the politician's office and responsibilities, some have more need than others to gain a solid understanding of other countries' political situations. A governor of a US state, for example, may not need to learn in-depth information about the politics of any particular third-world country.
Can someone who has studied up and has a solid understanding of the politics of a Third World country really know what it feels like to live in such a country? No. Some personal experiences can only be truly understood by someone who has lived through them. How politics "works", though, is something that the person with an interest or need to learn can learn.