I compiled 2.4.18-0.4 with CONFIG_X86_UP_APIC and CONFIG_X86_UP_IOAPIC enabled. The resulting kernel would not boot on a K6-III. Kernel initialization failed with the message "No Local APIC present". In the past, I've always compiled APIC support, and it's worked on the machines which support it and just been ignored on the machines which don't. This is also what the kernel documentation (Configure.help) says should happen.
I'm closing this -- later kernels haven't had this problem