Your measurements seem inline with what jota_1939431 measured during this test: The specified item was not found.
Deep_Sleep (HIDOFF) is not supported while the connection is up. However, a connection can be kept when sleep is enabled (but not when deep sleep engages). When the device is connected/scanning/advertising, it will always sleep between RF activity if the application allows it and there is sufficient time before the next scheduled activity.
There is alot of good information here in the section of threads classified under the sleep category, some even include sample code and explain how to verify the device is actually in sleep mode: WICED Smart Forums
Deep Sleep between advertisements is not advisable.
Power may be reduced using a DC/DC converter.