The logo was checked in its entirety, not just the checksum, but the gameboy would read it twice: first to show it and then a second time to check for its integrity (and if it failed, the console halted). This meant you could display a custom logo and then return the unmodified logo to the console's firmware so it wouldn't halt.
I think the entire defense relied not on whether you could show the nintendo logo on boot but on whether you could embed it into your ROM. It's the same as Sega's TMSS https://segaretro.org/TradeMark_Security_System#Purpose