Only for a certain amount of time, I think 5 days. And if you are installing the same software on a different GP, you have a new ID so you will have to buy the same software again, unless you resort to other drastic measures. Personally, I think Ent software or whoever should come out with a method of allowing users who can prove ownership of multiple GPs, the ability to transfer software they have purchased to any of their GPs. Typically, this only affects two crowds, the ones who have the most invested in GP, by purchasing a non-flu and liking it so much they go out and purchase a flu, and the other crowd, those who steal from the community with the intention of playing for free. Unfortunately, the method of protection that was chosen punishes those who support the GP community the most. Those who never intended on paying, will never pay and will play for free!
Just my 2 cents.