You can tar it if you want, but I'd just copy the whole thing over the lan to the new destination. I think I would skip /tmp and /var/run (in fact, look /var over carefully...you can skip a lot of it) as well as /dev and /sys, but when you do that then, yes, your system will run on the new hardware.
You'll probably have some minor issues - like in fstab and possibly with some network config things - but nothing big, presuming you are using a stock kernel.
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