Does the CH340G actually go into suspend mode

The datasheet suggests that some CH340 parts support going into suspension mode when there's no activity for a few ms. And I've seen references here to the "power down" mode of the CH340G. But I'm having trouble figuring out if that's actually happening on my Nano lookalike.

I've removed the power-on LED from the Nano, and I also have a separate USB-to-UART adapter module that uses the CH340G, and its power-on LED is also removed.

Connecting the module to USB, but with nothing connected to it downstream, I see a current draw of 12.1ma. That clearly isn't in suspension even though there's no communications going on.

When I remove the Nano from the breadboard, so that it is connected only to USB, and running a sketch that prescales the system clock down to 1 MHz and spends about 60% of the time in Idle sleep mode, I get current of 15.5ma. If the Nano's CH340G is also drawing 12.1ma, then that leaves only 3.4ma for the 328P and the voltage regulator, which actually seems low. So that would indicate the 340G IS in suspension, but it doesn't explain why the adaptor doesn't do that.

Can anyone clarify this situation? Does the CH340G go into suspension? If not, is there a CH340x that does?

Also, is there a low-power demonstration sketch that puts the 328P as much to sleep as is possible? With that, I could maybe lift the pins on the voltage regulator and then see what current remains.

Nick Gammon's low power post.