No, in that large universe model we'd expect to be part of one of the expanded, intergalactic civilisations, and not part of a small, still-at-home civilisation. So, as I stated "we would not expect to see the world as we do in fact see it". Clearly we could still be part of a small civilisation (nothing logically impossible about being in a tiny minority), or we could be in some sort of zoo or ancestor simulation within a big civilisation. But that's not what we'd expect to see. You might want to see Ken Olum's paper for more on this: http://arxiv.org/abs/gr-qc/0303070

Incidentally, Olum considers several different ways out of the conflict between expectation and observation: the finite universe is option F (page 5) and that option seems to me to be a lot more plausible than any of the alternatives he sketches. But if you disagree, please tell me which option you think more likely.