No, you can't. Without that little "hack", if you boot from the LPC, it won't look anywhere but the LPC for a FlashROM chip (i.e. the TSOP). You have to follow the directions that are now infamous or it simply won't flash to the TSOP.
EDIT: If you don't want to do that hack, you can always boot up your XBox without the modchip on and use the 007/MA gamesave exploit to flash the onboard TSOP. This requires you to solder two points, but that's a helluva lot easier than soldering the wires and getting the timing down. This is all assuming, of course, that your TSOP still works and you can boot your XBox up unmodded.
