Nope, you only need an HDMI system on a Surround Receiver to take full advantage of the High Definition audio formats (Dolby TruHD etc). And even then the HDMI version needs to be 1.3.
My current surround system doesn't have any HDMI inputs on it at all and I still get great surround sound from my DVDs, HD DVDs, Blu-ray Discs, and Xbox/360 games.
You'd be better asking this question in the Surround Sound forum though.