No, uninstalling and reinstalling might not make any difference I believe, but you certainly wouldn't have to download it again. If you chose to reinstall just use the setup file you downloaded already, uninstall, reboot, install, reboot.
At no point do you mention what type of scan or settings it is that you are doing ?
I assume by full you mean, Local Disks, and I'm guessing you have the Sensitivity set to Thorough and include Archives ?
Archive (zip, etc.) files are by their nature are inert, you need to extract the files and then you have to run them to be a threat. Long before that happens avast's Standard Shield should have scanned them and before an executable is run that is scanned. Thorough is also by its design very thorough and perhaps a little overkill for routine use, were a Standard scan without archives should be adequate.
I have only ever done a through scan with archives once shortly after installation just to ensure a clean start state, but with XP for example avast will do a boot-time scan after installation if you select it, this I believe will be quicker and reasonably effective. Like everything in life things are a compromise.
