Assuming that every woman in a burqa has passed a test while wearing it (and presumably the proportions of illegal unqualified drivers are the same for that group as for others), then presumably they can see enough to pass the test, IE as much as anyone else? (whether the test is sufficient is another question, of course.)
I think given the tiny proportion of drivers in that category, compared with the larger proportion of bare headed 'can't be arsed to look' merchants, it's small risk.
Assuming we mean the scarf pulled tightly around the eyes and face, and not the full one, I'd have thought it restricted peripheral vision less than a loose scarf, or a big hairdo. Have we established whether the OP meant this sort, (actually a niqab) or the full scale robe with mesh to see through? That I can imagine would cause problems, because the head could move inside it, like inside the hood of an anorak.
BTW, in Googling for images to confirm the names, I think I might have accidentally clicked on a BNP type blog. I feel dirty now.
