Agreed. Low and slow. But... this doesn't address if your nudis will be effected by the fluconazole. Trying to remove any livestock from an established reef can prove difficult. Odds are that you won't be able to remove all of your berghia prior to treating for the bryopsis. So the question still stands.
I have used fluconazole in my own systems several times with mixed results. Not once have I noticed any negative impact on inverts in my tanks. That being said, I have never treated with berghia nudis in the system.
I presume they will be fine, aside from being hungry from no longer having any Aiptasia to munch on.