Does android, specifically the HTC Incredible, support headphone volume buttons?
Definitely supported by Android, and I'd be incredibly surprised if the Incredible didn't support volume control. 

I had no problem using the volume control buttons in the headset I bought for my G1. I bought mine on eBay for $7, it has no branding but was marketed as explicitly for the G1. It uses the USB plug, not the 3.5mm plug. 

You might need a USB headset.

There is something specific about apple's 3.5mm jacks that doesn't play well with non-apple devices. Something about the placement of the insulating plastic bands. It is described in the answer to: Why can&#39;t I use my iPhone Headphones with my HTC Thunderbolt? 

So it wouldn't surprise me if a headset from your iphone with a 3.5mm jack would not work on your Incredible. But if you buy a headset manufactured for the incredible (Ebay and Amazon appear to have plenty) and the volume controls still don't work, the problem is probably your device.