Yes, updating a Wii with a WiiKey modchip will likely brick the console. Official updates patch the firmware vulnerabilities WiiKey exploits, detecting the mod and rendering the system inoperable.
Modern homebrew (Homebrew Channel, USB Loader GX, Nintendont) offers better compatibility, no disc swapping, and update blocking via Priiloader. The WiiKey is 2008 technology. Migrate to homebrew for a safer, more capable experience.
Warning: Bricking is often irreversible. If unsure, don't update. Seek help from Wii homebrew communities before attempting any hardware modification.