Short answer: If you write the software yourself, then yes. Using existing software, no.
Searching for "power down PCIe card" shows that you are not the only one looking for this capability. Some of the results, for example "Switch off the discreet PCI-e vidcard" (what a sweet typo!) state that it is impossible, but do not back this up.
Others such as Anyone know how to power-off a PCIe slot? (eg. video card) approach this more seriously, but did not succeed.
There's even an existing question about this here, Is it possible to power off a PCIe video card/slot? (eg. hot-plug), without a solution, though (you should have mentioned that! ;-).
You state HD6700 in one place and HD6500 in the other. Which one is it?
The actual model names have at least one more significant digit. 6570, 6750, 6770 and 6790 all have different idle power draws.
According to http://en.wikipedia.org/wiki/Northern_Islands_(GPU_family)#ASIC_table,
the power draw is between 10 and 19 Watt.
19 Watt is not much, but apparently still needs active cooling.
You said that you want the fan off, so your underlying problem is apparently its noise.
You might be able to lower the fan speed using ATI-specific software tools (I have NV, so don't know which ones would work for you).
My guess is that desktop operating systems nowadays do not care enough about this amount of wasted power, and simply do not support turning off the power of a PCIe card.
(But they should, in my opinion.)
If you are really interested, you could look at what mobile device OSs such as Linux (including Android), are doing. They dynamically power up and down devices to save power.
On the GTA04-owners mailing list at least there are several discussions regarding how to power up and down devices like wifi, bluetooth and others. They at least know how power control interfaces look like under Linux. This might help you find out whether this has ever been implemented for PCIe devices.
Depending on how often you need the discrete card's 3D power, your best option might be to remove the card (as you said). Or put it in a separate PC, that you boot only when needed.