The only application I have on my Mac that works with PhotoStream is iPhoto. I'm wondering if my Mac grabs the images from PhotoStream constantly or if it only downloads them when I launch an application that uses PhotoStream (such as iPhoto).
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/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