Purchased music on a computer that temporarily has no internet connection to reauthorize.

Hi,

I had to deauthorize all computers to remove two devices that no longer work. I was able to reauthorize two of the ones I needed to but forgot that the wifi chip on my desktop, which is what I sync to as it holds all of my music, blew out. I cannot at this time connect it to an internet source to reauthorize the account. However, I would like to be able to update my ipod with the new music that I have, but I don't want to lose the ability to play what I already bought. If I sync my ipod before being able to reauthorize the computer, will I lose the ability to play what I already bought until I am able to reauthorize it?

-Thanks