I'm uploading a 6GB video file for a friend, from my machine into a shared folder that they own.
Once the file is uploaded to the shared folder, can I then delete it from my machine, without also deleting it from the shared folder?
No. A Shared Folder is exactly that; if one person deletes a file from the Shared Folder, it is deleted for all the people for whom the folder is shared.
To do what you want, you'll need to wait for the file to finish transfering, then disconnect from the shared folder. (In the web interface, right-click the shared folder, choose "sharing options", then "Leave folder".) Once the folder is no longer shared, then it's safe to delete the file from your Dropbox folder.