Would Anne and Peter have formed such a relationship if world circumstances were different?

No, Anne and Peter would not have formed such a relationship if world circumstances were different. Anne and Peter knew each other to say "hello" before going into hiding, but had nothing in common in the "outside" world, and given the difference in their ages, as well as schools (Anne's life outside the annex revolved heavily around her own school), it is most doubtful they would have ever even become good friends.