Analog out from a computer is probably not analog copy protected. Here's why:
(1) It would just add more overhead to the bandwidth of the stream
(2)
Amazon probably doesn't really care about low-def analog copies
I've done this in the past for iTunes.
The biggest issue is the computer interrupting the playback. Turn off all anti-virus, system updates, email, etc. On my main system, this would be a huge PITA. On my lean capture system, which already runs almost nothing, this is no issue.
Only the Blu-ray/Roku type devices would attempt to block the signal. I'm not sure how those work, but I believe the device itself is responsible, not the stream. It's why WDTV doesn't really block anything.