Nope. You would have to change every command that loads from the CD to load from the HDD. XBox is much easier to program for this because it is x86 based just like a PC. The DMS3 modchip has a new mode that loads HOMEBREW apps ONLY off the HDD, such as the Genesis emulator PGen. New PS2 Gaming HDD's are coming out soon that load commercial games off the HDD, but they are MagicGate encrypted (just like the stuff on your memory card) so you won't be able to load non-licensed backup games on it. Also, I've heard if you plug the PS2 Beta Gaming HDD into a PC, it trips off part of the PS2 partition and when you plug it back into the PS2, it asks you to reformat it because it knows its been tampered with. So, in a long answer, no, and it doesn't look that way for a while, having a proprietary MIPS based console opposed to XBox's PC-in-a-console design gives Sony the upperhand on some things.
-US Nintendo Wii unmodded (waiting for modchip and install)
-US Playstation 2 v15 SCPH-77001 w/Crystal Chip Pro 2.0
-US V1.0 Xbox w/Xenium Ice and X2 custom BIOS