Would Westerners stop their wars and occupations of other countries, abjure targeted assasinations, abductions and torture of suspects and give up support for apartheid style regimes like Israel?

With an entirely secular government? I'd be surprised if at least some of these things didn't happen.

Tony Blair used his Catholic religion - the one he lied about and kept secret from the electorate - as an explicit excuse for the Iraq invasion.

Of course there's no guarantee an atheist would have thought differently, but 'god' does seem to have an odd habit of getting involved in wars everywhere.