This sounds similar, although not the same, as the problem I have had with HDMI.
I plugged my newly delivered A600GS which arrived last week into my TV, which is a Samsung from 2009 (it has only 1 HDMI port and is literally the only digital connection on it - everything else, including the TV tuner, are all analog).
I use this TV with a digital PVR, The C64 (from Retro Games Ltd, not a real C64) and occasionally a Dreamcast, which all have to share the HDMI port (I swap the cables over each time, as my PVR doesn't like using a multi connector box).
Anyway, just like your issue, sound was working fine in the menu but not at all on the Amiga side (so AmiBench or any other game/application). Changing it over to rear audio socket and plugging a pair of headphones in the 3.5mm jack resulted in 100% perfect sound in everything.
All the other devices I connect to my TV HDMI work flawlessly. This is the first time I have had an issue with it.
I found the thread about changing the resolution to what the A600's display settings said was the TVs native display mode, 1680x1050, but still there was no sound at all through the HDMI on my TV.
After that I tried connecting it to my PC monitor, an ASUS VS247H, and found the sound works perfectly through HDMI with that and all is lovely with it. So that is now what I am using when I want to use my A600GS.
Someone told me I should have a look at my TV settings, but I honestly can't find anything in there, either in the TV settings or the manual that relate specifically to HDMI. Maybe that might help your situation though.
Anyway, while I can't really offer any suggestions or solutions to your issue, I can answer your question:
YES, I had the same issue, with sound working in the menu but not the Amiga side, which I solved by using a different display.
NO, your A600GS is probably not faulty, but I can't tell you what the problem would be.
If you have/can borrow a pair of 3.5mm headphones, try it out with that and you will most likely find you get sound that way.