Potentially, yes. But only if the first-place candidate didn't get >50% of the votes on the first round. Those who vote for the last-place candidate (who is eliminated) have their second choices taken into account. This keeps going until one candidate has 50%+
I agree 100% with theoldbrigade's fears on 'manifestos going out of the window'. Maybe not so much with AV but certainly PR. The result may be fairer and more representative on paper but even those who vote for the bigger parties don't get quite what they expected - as we've seen in the last year. PR is marketed as engaging more people in politics but I could see how a built-in post-election blurring of commitment would put more people off.