I am 95% confident you don't actually need to assign IPs. Do this:

  # ping all link-local devices on an interface:
  ping ff02::1%eth0

Oh, I had no idea you could perform such a "broadcast" ping on link-local addresses. Now, that is a nice trick that will save me some typing between computers.

mDNS / Avahi is also great if the machine advertises itself: just use machinename.local after plugging it.

Though the interface needs to be configured for link-local addresses. In my experience, NetworkManager now periodically resets the link if it can't get a DHCP server to respond. I understand the rationale, but it used to be simpler to plug into a headless machine and be confident that you could just ssh in.

I would assume so as well, I'm not sure if all host operating systems act the same though. But you could probably just wait a couple of seconds and the interfaces would have assigned themselves link-local addresses.