Mine does not.
As long as the USB cable is connected, the system has a "wake lock" set -
It will show a screen saver when the time-out tells it to, but it does not go to sleep and it will not drop USB networking (or the sshd or telnetd processes).
Now this is on the original 5.6.1.1 firmware - I haven't upgraded my device.
(I could give a rat's ass if it can use Amazon services or not.

That is incredibly low on my 'features to support' list.)
= = = =
See:
https://www.mobileread.com/forums/sho...5&postcount=14
You can see that the CRxxx devices are not installed.
In that pic - I sort of made the engineering level tag unreadable with the glue blobs.
But there is a second "PW-3" (tagged) thread with close-up pictures (of both PW-3 and PW-2) if you want to look for differences in mounted parts.
Oops - I was thinking of:
https://www.mobileread.com/forums/sho...d.php?t=249979
but the on/off and reset connections work on that device also.