Yes. You can deploy SharePoint solutions on the Extranet. I know several small and large customers who either have deployed a SharePoint solution externally or are in the process of doing so. A few months ago, we released a whitepaper relevant to partners and customers who want to deploy WSS on the Extranet. You can find it at http://www.microsoft.com/technet/prodtechnol/windowsserver2003/technologies/sharepoint/revproxy.mspx. There are several other resources, one of which, is a web cast that you should view at http://go.microsoft.com/fwlink/?LinkId=28245. And of course, the SharePoint Products and Technologies Resource Kit is another great resource.
One of the most frequently asked questions... where is the SPS Extranet Whitepaper? It's on its way. We expect to have it published early next calendar year on TechNet. Another topic, that is very relevant to SharePoint Extranet solutions is Best Practices for Multi-Tier SharePoint Development - specifically, how to develop Web Parts and Custom Site Definitions and move them between dev, test and production environments. That whitepaper will also be available by early next calendar year on MSDN. I recommend subscribing to the SharePoint MSDN RSS feed so you know when it's available.
Besides technical guidance, you should also look at the licensing guidelines very carefully to understand how WSS and SPS are licensed, especially when it's deployed in an Extranet scenario. Licensing information can be found from http://www.microsoft.com/sharepoint