Can you perform batch edits in Aperture?

You can indeed, although it's a little counter intuitive.

What you do is edit one photo with the adjustments you want to apply to all the photos. Then you click the "Lift Metadata and Adjustments" button down at the bottom of the screen, near the arrow and crop tools and such.

A new window will pop up. You will see some drop down menus and tick boxes. Select the ones you want to copy to the other images.

Now select the photos you want to apply the changes to and click "Stamp Selected Images" and Aperture will apply the changes.

Also, you have discovered the peculiar way in which Aperture does selections. While you can select multiple images you can only make changes to one image at a time, which is denoted by a thicker while outline.

Yeah, here's a mini tutorial video...
http://www.apple.com/aperture/how-to/#video-stamp

I use the lift and stamp method already suggested.

BTW, I think you can also apply certain things on import. Towards upper-right in the import screen, there's a button that lets you add additional modifications to apply to the images being imported. You can also save that as an import preset or default.

yes, you can save also as preset and then use it either during import or when you need it for EACH image.. in batch mode only lift and stamp works..