Hmm, interesting idea. You can do it although it needs a bit of setting up.
First, create a search channel. This will create a new channel that gets the results of the search once an hour (for example) as a feed.
Then, create a channel report that simply dumps the content of the search channel to a file on the network. Alternatively, Awasu always keeps a copy of the last feed received for every channel in the Logs sub-directory so you could periodically copy this file up to the network. You would proably want to run an XSLT on it first to convert it to HTML or something like that.
BTW, channels can be configured to send emails when new items arrive on a channel so if you're doing this manually right now, you can instead get Awasu to do it for you instead
Actually, that gives me another idea. Blogging systems can often be set up to accept posts via email so if you get Awasu to email new items to a blog, people can monitor your search results there as well. Definitely cool