No. The ATV 3 does not have accessible storage, it is simply caching the stream temporarily. If you access other content or turn the device off the content will be flushed and require reload.
If you are receiving a sustainted rate of 5mbps (can be verified at speedtest.net) then it shouldn't be too long before it is 'ready to watch'. You don't have to wait for the full film to load.
If you want to store the film for later viewing you can rent on your computer and stream via home-sharing.
So.. just so I understand this... the ATV only downloads the movie to be played right away. If you interrupt the download by, lets say switching your input to watch regular TV, it stops, even though it's still connected to WiFi, and when you turn it back on, it has to start the download over from where it left off.
I had thought that the movie downloaded to the ATV and was ready to watch at any time. We had started the download last night and it was 'ready to watch' - and we watched it for about an hour and then it stopped. We had caught up to the download. I left it on and we went to bed. I thought that we could resume the movie this evening because it would have finished the download - but no, it resumed the download from where we had left off.
So.. since we're on a slower than normal hi-speed, we should rent the movies on the computer and then stream them via home sharing. Does that sound reasonable?