Can a PC boot without a GPU of any kind if it is using software rendering?

Me and my friend were arguing earlier about whether or not it's possible to use a computer (at all) without any kind of GPU, which he thought was impossible. So I told him about software rendering and headless systems, but he said then the system would fail to boot before it could start using the software rendering. I didn't think about that and wasn't sure how to get past that, but I insisted that it was possible because then systems such as servers would not boot, which I would presume many don't have GPUs at all (they would be using a server CPU so no IGPU and they wouldn't need a dedicated GPU probably).

It's absolutely common - many routers and NAS boxes would qualify as computers even under restricted definitions, and they don't have any GPUs. (But run pretty much any Linux app you care to mension).

A fair number of computing devices have some variant of serial cable which can (optionally) be used to debug a boot process.

Many headless systems can be network booted and loaded with a full OS install, including regular PCs with no onboard or discrete GPU.