Bit-reversal equivalence on IFFT (radix-2 Cooley-Tukey)
To answer my own question : no you can't use the exact same algorithm. 

In the case here of a decimation-in-time, radix-2 Cooley Tuckey, in-place FFT/IFFT algorithm, we have the choice between two implementations which are exactly equivalent :



The above uses bit-reversed inputs and produce natural order results.



The above uses natural order input and produces bit-reversed outputs.

You can see that the operations are the same : for each butterfly operators, same input data, same twiddle factors. It's just the address of that data (here, the number of lines from the top) that changes.

The same applies for IFFT. When applying the bit-reversal after the IFFT, I would have needed to change the IFFT algo so that it changes the addressing scheme to match the second algo.

To go a bit further on the topic : "ALGEBRAIC FORMULATION OF THE
FAST FOURIER TRANSFORM" from Tran-Thong. (http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&amp;arnumber=6323745)