I think getting around permissions would be an issue but when I was starting on Linux I remember there was a way to install to Fat32 inside a directory in parallel with Windows 95. The distro was called Phat, so the concept is not exactly new.
I think it was Ygdrassil, or maybe a free distro off of a CD. Great investment of time as it got me into the oilfield doing tech support. Running Rocky 8 on a P1 Gen4 now, so come a long way from my 486/Dx2.