(Answer requested by Kacey Mae)
Can it? I suppose.
But it would be extremely difficult to pull off at all; and nearly impossible to pull off in a way that would fool anyone who was paying attention.
The usual way to run a full 32-bit OS inside a full, operating 64-bit OS is to use a virtual PC (info; example). But such software isn’t subtle — your PC’s hardware will be simultaneously supporting two complete operating systems, with all the added overhead and resource use that implies.

running in a virtual PC on my current 64-bit Win10 setup.
If you attempted to wrap a virtual PC in some kind of “virus,” the resulting code would be huge (it would need to contain the entire second OS, plus the virtual-PC software), would take a while to set up, and only the least-observant users imaginable would be fooled by the process.
Besides, most 64-bit OSes (e.g. Windows) can already run 32-bit apps — that’s “backwards compatibility,” and it’s baked right into the primary software; no helpers or viruses needed.
Running an entire 32-bit OS inside a 64-bit OS is not a simple or subtle thing. And trying to do that via a virus? I think you’re barking up the wrong tree.
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