No, and this is one of the more difficult things for non-technical types to understand.
Each core operates independently of the other (more or less), and each one operates at 1.6GHz. That is NOT the same as a single core 3.2GHz CPU.
So just as a kind of example, say you run a restaurant. You have one person who can make 3.2 salads an hour, and two other people who can make 1.6 salads an hour. The benefit to the two people working slower is that each one can be making a different kind of salad, and if one of them calls in sick or goes on break, you aren't left without a salad maker.
Or another way to look at it would be that a single core CPU would be like a single lane highway with a speedlimit of say 60MPH vs a two lane highway with a speed limit of 30MPH. If there's an accident blocking one lane, traffic can still get by on the other lane.
Parallel processing, which is what you have with dual and above core systems, is more about performing a number of tasks at the same time as opposed to trying to ram each task through as quickly as possible. The result usually is that your system may be a little slower, but the overall experience is much smoother and more consistent. Even if you have some large task going on one core, the various processes that are needed to make the OS work, can be handled by the other core, so your system is still responsive and usable.
If I had a dual-core processor (let's just say, hypothetically, that it's the AMD Athlon here: http://emachines.com/products/products.html?prod=ET1331G-07w), and it's clocked at 1.6GHz, wouldn't it actually be 3.2GHz because it's dual core? Thanks!