Can a 1.6 ghz dual core processor run a game that reqires 2ghz single core processor

Yes it can. I've done it plenty of times (my computer uses a 1.8GHz dual-core). I've played UT2004 and Need for Speed Most Wanted fine on it. Mind you, if your computer has a 1.6GHz processor, increase the RAM to the maximum supported, it really helps.