Sure. This is called "progressive download" and is fine for short movies. There's no need for a streaming media server unless you have long movies that you want your users to be able to index into.
That seems to be the trend. Adobe claims that it has the greatest reach of any format.
There are lots of tools you can use for conversion. If you don't freak-out at command-line tools ffmpeg will do a decent job. However, it doesn't support ON2 VP6 (which needs Flash Player 8) for writing (ffmpeg reads VP6, but doesn't write it), which may not be a big deal.
I suspect it will shortly support the LATEST flash codec (H.264 - needs Flash Player 9 version released December 3, 2007) since that is just a matter of wrapping H.264 (which ffmpeg does support quite well) into a flash container. But it will be a while before the latest plugin is widely deployed.