I'm not really familiar with the typical set up in a refuge camp
There is no typical camp, and no typical refugee. Some of the people fleeing violence at home are already well educated. And some settlements have more reliable utilities -- and thus are more suited for telework -- than others.
Or would people need to trek to the closest city?
Not a matter of trekking; some of the refugee centres managed by UNHCR are located in urban areas. I was at one in Kampala last week.