If I were to delete all of the pictures on my photo stream, would I still be able to keep the copies on my camera roll, or would they also be deleted from there?
The camera roll on an iOS device is totally independent of your photo stream.
So, if you have an iPhone 6s for example, and you've taken 1,234 photos on it, these photos will remain in your camera roll until you have manually deleted them yourself. Even if you have used iCloud's Photo Sharing feature to share 500 of those photos and then decided to delete them from the shared album, those photos will remain in the camera roll unless you delete them from there as well.
In a nutshell, any photos taken on a particular device and stored within that device's camera roll will remain stored in that camera roll until they are manually deleted from that camera roll. It is irrelevant whether you have deleted them from a photo stream, a shared album, etc.