Not from the very beginning. The earliest live boot CD I remember is "DemoLinux". Back then that was still a major hack. Now Fedora, at least, boots into live mode to run the installer from the full GUI.
Yggdrasil Plug-and-Play Linux supported running off the CD as far back as 1993, but you needed a boot floppy because computers couldn't boot from CD at that point. When you installed it to your hard drive, most of the included software stayed on the CD, meaning that you had ~500 MB of software and source code permanently available without taking up hard drive space. This was useful in an era when 200 MB and smaller hard drives were common. After installing, you could pick and choose which system components you wanted to move from the CD to the hard drive.
