I would not be comfortable making such assumptions on the topologies of fitness functions in high-dimensional spaces. I think it was not so long ago when I read an article here at HN about how weird the high dimensional spaces are, but can't find that quickly.

Further, the mindboggling size of the high-dimensional spaces make me all but guaranteed that not a single non-trivial neural network made by homo sapiens has ever been in global maxima. But I have nothing but my hunch on this.