Firmware is using cache as RAM (e.g. https://www.coreboot.org/images/6/6c/LBCar.pdf) to do early init, like DRAM training. I guess later things in the boot chain rely on DRAM being set up probably though.

I would be pretty curious about such a system. Or, maybe more practically, it might be interesting to have a system pretends the L3 cache is ram, and the ram is the hard drive (in particular, ram could disguise itself as the swap partition, to so the OS would treat is as basically a chunk of ram that it would rather not use).

That would require either rewriting drivers to never use DMA or making sure that all DMA controllers are able to write into and read from L3 directly.