In other words, there's no real difference between a modchip and booting the game from a disc. Even though not all games will boot from the Utopia disc [Sega Extreme Sports for one], there are other discs that should work fine.
The Game Shark / Action Replay discs work aswell. If you set the boot mode to NTSC, the program will prompt you to change the disc and the system will reboot. The DreamCast logo will now appear red.
I'm not so sure if installing a modchip is worth the trouble, if it works like you've described it [patching region only at first boot, and doesn't work on multidisc games].