Yeah the naming is definitely confusing - they need to pick abstract words or nouns for products
The new thing that they just released is actually a phone dialing extension to Google Talk or Chat : gmail.com/call
Google Voice comes from Grand Central and is the service that they initiated in April 4, 2009: google.com/voice
And to make things more confusing, the two can integrate.
Back to the OP's question: if on your mobile browser you go to the full "desktop" website for GV, then it works as I described above on Android (tested on the N1), on the iPhone, and I just tested it on the iPod Touch and iPad - it worked fine on both.
So while I don't actually have a Desire in my possession, I see no reason at all why it wouldn't work. I'd say it's almost a certainty that it would. TKG: if you have a GV account maybe you can try from the "desktop" web page and confirm for us.