Since the modern Linux kernel doesn't make any promises of 486 support there's very likely plenty of places inline assembly uses instructions unavailable on a 486.
So even if you compiled it with strict -march i486 you'd end up with unsupported instructions. Modern GCC also doesn't like emitting strict i386 or i486 code anymore so you'd be likely to end up with unsupported instructions even without any inline assembly.
I don't know offhand what instructions were introduced in Pentium or later.
Doing some googling... 486 had cmpxchg, that's good.
Seems it didn't have rdtsc. It's not out of the question, I might say even pretty common, for user mode code to use that one via inline asm to implement a timer.
Obviously no SIMD instructions. If they say they're supporting 686 or better they might have some compiler flags that depend on mmx or similar? SSE came late to P6.
So even if you compiled it with strict -march i486 you'd end up with unsupported instructions. Modern GCC also doesn't like emitting strict i386 or i486 code anymore so you'd be likely to end up with unsupported instructions even without any inline assembly.