How would something like this work? Is the target laptop running any random linux distro, and rsync replaces all system files etc. effectively "swapping" operating systems? Can the laptop boot into the new system as if it was installed normally?
This is pretty much how you install archlinux normally, except instead of rsync-ing the initial filesystem you make a new initial filesystem based on the "filesystem" package.
Just be careful if you intend to keep the old system running. You probably don't want to clone /etc/machine-id and similar (see: the problems that come with exactly cloning VMs). But of course, if the old system is being destroyed, then no worries.
My Arch is from 2007 or so and had only a few hiccups. The last thing happened when MD5 was getting deprecated for /etc/passwd and the automatic migration to another hash algorithm was not working, which is obviously directly related to the age of the installation.
It is running on its third mainboard/CPU/GPU combo with maybe the fifth HDD/SSD.
That's pretty similar to what installation media does anyway, really.
[EDIT] Oh you might need to install the bootloader too. But you can sort-of (your running kernel will still be the installation media's) do that from the rsync'd system once it's copied over, with some creative chrooting and mounting. Which, again, is something that Linux installers kinda do anyway, in ordinary operation, but you'd likely want to do it manually in this case. It's exactly what you used to do (probably still do?) installing Gentoo, even for a "stage 3" (least-painful) installation.
Very well and very easily. You can do that even with Windows, even with different CPUs: I've ported my master Windows install from a Xeon to a regular Intel CPU on a laptop.
This laptop still feels like downloading Xeon-specific updates time to time, but every system peripheral is recognized in the device manager, and everything has been working great for over a year now.
For my next laptop, I'll do just the same: use bitlocker unlock, clone this Windows install into a larger SSD using Linux NTFS tools, plug the new SSD into the new laptop.