Does PhotoStream sync to my Mac when iPhoto is not open?

Yes! A process called PhotoStreamAgent runs at login, and idles in the background, downloading new photos when they're uploaded to your Photo Stream.

There exist both /Applications/Aperture.app/Contents/Library/LoginItems/PhotoStreamAgent.app and /Applications/iPhoto.app/Contents/Library/LoginItems/PhotoStreamAgent.app, indicating that this background-downloading behavior works no matter which application you use to manage your photo library.

(And as Asmus points out, photos are stored in ~/Library/Application Support/iLifeAssetManagement/assets)

The photos are "constantly" downloaded to your Mac, and stored in subfolders within ~/Library/Application\ Support/iLifeAssetManagement/assets/sub.