Have you tried to run i386 installer on modern 64 bit hardware?
If the installer starts without SIGILL, then you can install it on
modern hardware.  You need not install it, just check if it starts.

Searching google appears to suggest that they are backwards compatible, e.g. [1]

I have the partial result that i ran the debian live i386 iso on 64
bit qemu architecture guest OS.

The answer might depend on the exact definition of "64 bit CPU".

[1] https://www.pcmag.com/news/32-bit-vs-64-bit-oses-whats-the-difference

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