I think a strategy focusing on great people can be viable - especially great scientists and great engineers, they can really make you leapfrog forward by saving many turns.
Is it useful to focus production on great people? Yes, I think it is. I've been experimenting lately with creating cities that focus on one type of great people, in order to generate them quickly. I think only the first few cities, the "major" ones, are appropriate for this strategy.
What you need is to:
- Build the city next to a river or lake, in order to be able to construct a garden.
- When you choose which wonders to build, make sure they all generate the same great-people type.
- Obviously, try to get as many relevant specialist buildings as possible. I think, however, that it might be better to let the city grow for a while before you transfer citizens to become specialists.
Wonders are important for this strategy, so try to focus on them (and maybe also use Egypt and/or the +% wonder production social policy). The patronage social policy that grants great people from city-states is also nice, though a bit hard to get.
Though I haven't played a full game like this, on one of my games I have made an attempt to focus my capital on great engineers, and the results were pretty good.