No, 7.6.1 has absolutely no support for 24 bit mode (hence why you can't run it on any 68000 system, or a SE/30, II, or any other 32 bit "dirty" system). However, if you drop that 550 to any version between 7.1 and 7.5.5, and you should have it - my LC III is running System 7.1, and I can confirm it has it.