There are several technical and economic factors that will determine the impact of this "black box fusion technology"

1. Economics - will this technology be cost effective versus existing conventional technology?
2. Economies of scale - is the technology economically competitive at small scale or does it require large scale like conventional large nuclear fission plants?
3. Ramping capability - consumption of electricity changes on a continuous basis. Will the fusion technology behave as a base load generator like existing large coal/nuclear fission plants or will the fusion technology be able to change output quickly and economically? (this assumes that large scale energy storage is not available)

Assuming "where energy demands are the greatest" implies third world economies, then the technology will need to be competitive at small scale and have the ability to ramp to match consumption.
Another scenario is to deploy fusion in developed economies. Then the competition is well known and the analysis of impacts is straight forward. There will be winners (fusion) and losers (fossil fuel, fission nuclear)

Hi Sandy,
In addition to Micheals first point, the economics will depend mainly on the investments and running costs. Historically nuclear and coal require an high investment, but once build have low operating and fuel costs. A open cycle gas turbine is quite cheap to build but more expensive to operate because of efficiency and fuel cost.
So if you needed to build generation to cover base load demand (i.e. demand that is Always there), The plant would run most of the time and thus the operating time is most important. If the plant was build to cover peak demand, operating cost would be relatively less important compared to the investment. It would not make sense to build an very efficient very expensive power plant that will operate only a few hundred hours per year.
This explains basically why there is not one most efficient technology. Each technology has its niche. 
With increasing variable renewables (which have almost zero operating costs and thus will produce once build if there is sun, wind and demand) running hours of other generation will decline, meaning that capital intensive generation (which require a large number of operating hours) will have a harder time.
This reasoning is a bit blunt, but we published a paper a couple of months back among others about the economics of power generation in a wind/solar dominated system. You can find it here if you are interested: https://www.dnvgl.com/publications/future-proof-renewables-103549  
kind regards,
Marcel