I just noticed this thread. We actually have 2 sets of bi-fold doors in our showroom showing this exact configuration and to demonstrate that it is quite possible.
To clarify for anyone else who may read this, there is 1 door (2 half doors) folding to the left and 1 door (2 half doors)...
They have a page at http://www.distinctivedoors.co.uk/modern_methods about the construction of their oak internal doors which shows you that they are not solid oak.
I wouldn't touch solid oak doors as in the past I used to make them and/or buy them and I had about a 75% failure rate due to...