As long as you're talking about staying in the same family (x86, etc) then what you're describing is conceptually similar to simply removing the hard drive containing the Linux install and putting it into a different machine. Usually that kind of thing will work (assuming you're using a stock kernel) but where it can trip up is if the mobos depend on different kernel modules to support the onboard devices (sound, LAN, etc). If you attempted to do it with entirely different architectures (eg, transferring an x86_64 to a Pentium III) then that clearly won't work
I'd say just go ahead and try it. Worst case is that you find out it doesn't work.
If your interest is in having a Linux disk that you can take with you and use on any machine, I'd suggest a Live CD like Knoppix. I keep a Knoppix disk handy at home, the office, and in my laptop bag. It's just an incredibly useful tool to have
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