Think about it. He has a hard drive with valuable data that either has a partially corrupted filesystem or the underlying physical disk itself is slowly dying. The absolute last thing to do to a dying hard drive is to write data to it & then expect to read that data off of it, which is really what you are suggesting. The important steps are to attempt to repair the filesystem and copy the data off.

Windows, Linux, Unix, Mainframe, Mac OS, it doesn't matter. The loading of OS is only as slow as the media on which the binaries are on. The operational speed of an OS is dependent on the system's I/O subsystems: CPU, Disk, Network. If a OS is on tape, then loading the binaries into the system's RAM is going to take longer than if the OS is on a CD. Knoppix is on CD and the loading of the binaries into the system's RAM will take longer than if they were on HD. If a OS is loaded from CD, or tape, or from HD and the binaries are loaded into RAM, then the speed of disk to disk file copies or disk to network file copies will not be impacted. And even if it were impacted, the speed difference in the end would probably be both small & irrelavant since the whole point of copying files is to recover them, not to get the quickest data throughput.

To howitzer,
If Knoppix (Linux) is unable to mount the drive then you may need a third party tool like Norton Utilities Disk Doctor to diagnose the disk & see if revovery is possible. Please see if someone you know has it.