Yup. Done this many times.
http://www.shockfamily.net/cedric/knoppix/ Never was able to get linneighborhood to work, but the command line stuff all worked fine and the folder was available to the network.
Alternatively, most days it's just as easy to take the drive out of the computer and plug it into the new one as a slave. Then mount it and move all the files you want. For laptops you need a converter because the IDE cables are different. And of course you need a two plug ribbon cable for your drives or an empty IDE channel. Never done SATA yet...