No, the AVR350 will not accept any audio over HDMI, ie video only.
I'm quite weak on the technical side of things, but to my understanding, quite a few higher/high-end brands were "suspicious" (not quite the right word I'm after) about audio over HDMI around the time the AVR350 came out. I bought mine late 2006 - not sure when it originally came on to the market. I believe Meridian used their own digital connection for audio sources, and Denon also had their own digital connection on some of their kit. Naturally, things have moved on, and we are now several or more versions on for HDMI, so I assume things have progressed.