It's a pretty lax license, as the Planetside folks are pretty understanding of those situations. I've changed computer 2-3 times and havn't needed to contact them for new licenses etc none of that bs.
Basically a license is for one USER. So as long as the program is only currently being used by one person on one computer at a given time. What they don't want is someone buying it, installing it on like 4 computers, and having 4 different people running it and using it etc.
Also animation comes with 5 "render nodes", which means you can install it on 5 other machines and have them all running at the same time, as long as the other 5 are only being used as render machines and not for development of new scenes.
But yes, basically you're good to go with upgrades, you just install on new machine, plop your license in and your good to go. Planetside is more then happy to see people get computer upgrades and enjoy faster render times.