Yes. She responds just as if I had given her a voice command.
As far as I know, you are correct. It seems Amazon is adamant about keeping Alexa as an “instigator” and not as an endpoint. The only reason I have been able to get my Echos to do stuff without opening my mouth is because I use webCoRE and a second speaker to send verbal commands to my Echo. (sneaky, I know, but it works flawlessly)