To answer your question, the amplifier portion will NOT turn off. I believe it is class AB power, so it will still continue to continue to generate some heat, but not to the level of a class A unit.
What you don't mention is if you are using this for 2 channel or multi-channel/home theater. If only just for 2 channel, you are better off just putting the money into a new (or new to you) integrated amp. Most likely it will have a better preamp section than Lexicon's bottom line home theater receiver.
Also, I seem to remember, but don't hold me to it, that Lexicon got criticized for the RV-5 because they just rebranded/borrowed the internals from someone elses home theater receiver, similar like they did with Oppo's blu-ray player.