You can save the results in a floppy, but you'll need to edit the makefiles, in order to install in the floppy, or use configure with the -prefix= option. But before you engage in this task, I suggest you try to check if the live eval has all other tools - besides gcc - needed to compile successfully, like libs, ldconfig, etc... Otherwise, compiling may prove frustrating.
The live eval cd creates a ramdisk where the root filesystem will run. I guess, a default install of an rpm will write files to this volume (under /usr). This installation won't be there the next reboot.
There's this tool, rpm2cpio, which is able to extract rpm files to whatever dir you want. Try to look for it.