You'd be better of getting the Dock Connector to VGA adapter, because the HDMI connector will only output digital signals, not analog for VGA. Also, it will disable video that is DRM'd.
If you don't mind having your iPad 2 tethered to your display via cables then go with other's suggestion and use Apple's VGA dongle. You actually can use Apple's HDMI+power dongle but you will need a converter box that converts HDMI to VGA and can deal with the HDCP DRM protection. Check link at bottom. Product provides HDMI to VGA even if HDMI is DRM protected via HDCP. Not cheap, but you are asking such a converter to do some pretty sophisticated electronic manipulations. Businesses and schools commonly have commercial overhead projectors with no DVI or HDMI inputs...just VGA and composite. In these situations, such a converter can be a life saver if you want to display on your overhead projectors high def sources with HDMI output. I mention this converter also because iOS 5 will provide full bore wireless mirroring of your iPad 2. But, you will need an Apple TV2 to do this and the AppleTV 2 only outputs an HDMI signal with HDCP protection. So this converter will hopefully allow you to mirror your iPad wirelessly on a display with no HDMI or DVI inputs once iOS 5 comes out and you have an Apple TV2. Good luck.