Yes you can, but it's nice to have if you need to restore. You will have to go through the jailbreak proces again if a restore is needed. Otehrwise there is no need for the desktop blackra1n program.
You will not need to restore the phone after deleting blackra1n. They do not connect to each other once the jailbreak is a sucess.
If you have a 3Gs make sure it's an older model that doesn't need the teather jailbreak. If you power down the newer phones the jailbreak process needs to be activated each time a reboot is needed.