I found a solution that works on the DT. The following was a suggestion in a Droid Maxx forum and it works for the Turbo:
Set a screen lock such as key code or pattern and the option where the power button locks it. With the screen off, hit the power button once to go to the lock screen but don't unlock. Daydream should start shortly without the keys lit.
I tried it and it works perfectly. A couple additional suggestions. For Daydream to start, you have to have it setup properly (i.e. on charge/dock/both). In addition, if you want it to operate in landscape mode, you'll need to run Daydream first in landscape. Turn the screen off with the power button and then turn it back on with the power button while leaving it in landscape mode. Don't unlock it and Daydream will start and the capacitive buttons will remain off no matter how dark the room is.
Hope this helps...