As far as I know the reason you are asked to not be breast feeding when having IVF is that the drugs (particularly the down regulation drugs) dry up your milk supply pretty darn quick. I also don't think there is any info on whether the drugs do get into your breast milk (probably because of the side effect that you stop making any.......).
As I understand it when BF'ing your prolactin levels are elevated and these elevated levels can make it difficult or prevent you entirely from getting pregnant. So the IVF may not be successful based on that. I am waiting for my DD to cease BF so I can begin IVF#2. Its difficult as I want DD to have as long as possible BF (she is 15 months old so has had a good amount of time!), get my levels down to ensure success and get pregnant so DD and our next child (hopefully!) won't be too far apart age wise.