I'm sure there are some crazy work arounds if you try hard enough but I'm not sure why it would be necessary in most cases. Almost everything I watch on the Roku is already available on demand if I want to watch it again later. I can see why you would want to for PPV type rentals but I'm sure they use HDCP. I know I have gotten a HDCP error a couple times from Netflix when something didn't handshake properly.
Season passes of shows on Amazon or other services are not rentals. You are actually buying the show just like you would on DVD so you can watch it as often as you like. I guess there are some live Roku channels. What exactly do you want to record from your Roku.