Could you theoretically run Doom using synths?

I enjoyed the "are synths computers" question, but I think it's a bit vague.

So as a more specific question, could you run Doom using synths?

And I don't mean running it on the chip that's running the synth. I mean like how you can run Doom directly in Minecraft or Excel, not just on the same computer as those programs.

I imagine it would take a ridiculous amount of synths, but maybe you could find a way to create a turing complete setup with the required functions of

• if, then, else
• goto
• basic math
• arrays

After all, a wavetable is pretty much an array, so maybe that would serve as memory? I don't know enough about machine code to work it all out myself.