Yes you can. Especially when you use Lightroom 3 noise reduction.

I want to show you this picture again – a repeat, but now with full sized crops and re-edited with Lightroom 3’s magic noise cancellation.

Here is the cat, shot with my 7D and a 50mm lens set to f/2, at 3200 ISO. And.. pushed 1.67 stops.

Meaning I underexposed, and increased exposure on the computer. This results in the worst noise you will ever see, much worse than you will see when using the camera properly.

Here is a detail from it, in the original size crop with no noise cancellation. Click to see it at real size.

Cat's eye with noise

Now we apply 90% noise reduction. Magic:

Cat's eye with noise reduction

The finished picture:

Cat with noise reduction

So do not be afraid of high ISO when you need it. It’s fine. Relax.