Most would tell you "NO!" I would have to agree. You should never have an active internet connection without AV protection. Also, you should never disconnect from the internet and then turn off/remove your AV without first doing a full computer scan to ensure that there are no virus's hiding in your system. Always better to be safe then sorry.
With all that said, I've been online more times that I can count for a few minutes here and a few minutes there to download AV protection. As many times as I've done it, I've never had a problem or an issue. I always make sure that I have the AV site download page set to my home page, or at least bookmarked so that when I start up IE (or FF or whatever), I'm right there and can download it. Now, I'm not telling you to do this. I'm only telling you my own personal experience with it.
As an alternative, you could download the AV program, saving it to your hdd, then disconnect from the internet, uninstall the old AV, then install the new AV. You could also download the new AV on a different computer, save it to a CD or memory stick, then just transfer it over to the computer without AV and install it (copy it to the hard drive first!).
Hope this helps!
War produces veterans, wounded both physically and mentally. They have sacrificed for us.....and it is now our job to help these veterans, as they have already helped us in ways we will never know, in ways that we cannot fathom, and in ways that we take granted every day.