No, they will remain on your device. When they are in Photo Stream, they are "in the cloud." When you download them to another album, a copy is stored locally.
The part of the PhotoStream that you are seeing on your computer when you enable Photo Stream will take up storage on your computer. How much storage, will depend on when you enabled the Photo Stream.
All your Photo Stream photos your Mac is currently seeing in the PhotoStream, are stored in your User Library - in the folder