Yes - that would be possible. Essentially as long as the request has some means of entering credentials that will be authenticated before the request gets to the WebDAV module in ExecuteRequestHandler, then the WebDAV module will not be aware that you have implemented some other form of authentication. (Of course, this logic does not apply to Forms Authentication since that is not actually passing credentials via the HTTP headers, only through the HTTP request entity.) So in theory, if you wrote a custom authentication module that used cookies and a server-side mapping of cookies to user accounts that executed in BeginRequest then you authenticate a user on behalf of a cookie-based client.
I have to state, however, that anonymous uploads via WebDAV are not generally a good idea and I always recommend forcing users to log in. ;-)