Well I did it this morning - the results are, er, interesting!
Before I describe it, I should say that my hair is naturally very dark brown, with probably about 40% grey. It's in a shortish bob.
I have been using black or dark brown semi-permanents for years (the 24 washes type, like eg Movida). No permanents. I try to just do the roots each time, but the ends definitely have a build up of black on them as they are (or rather were), jet black.
So - it is now a very complex mixture of shades. The first two inches of the roots are a lot lighter than the ends, so I think it would take more than one application of even the high strength one to get rid of the build up of colour at the ends (the packet does say this).
The 'new' colour ranges from a light reddish brown at the roots through to a dark mahogany brown at the ends.
I KNOW that reddish brown isn't my natural colour, but I think what has happened is that that grey hair was too permanently stained for the stuff to effectively strip all the black off, so it is now this reddish-brown colour (the packet does say that it might not work on grey hair).
However, although I'll probably have to stick an ash colour on top to tone down the ginger, I'm generally fairly pleased that the black has mostly gone, so I've got something to work with.
I think the results for different people will vary a LOT depending on what type of dyes you have used before and how dark they were. Also how much grey you have.