The Moto adds a few extra phone and carrier specific voice command options, but will still default to the regular Google Now Voice search for all the regular stuff Google Now / voice search already does. Using the Moto Voice say your command and then "show list of commands" to see a list of Moto Voice commands... but keep in mind anything else you ask it will still work by defaulting to the regular Google Now Voice search. But yes you can enable the regular stock Android / Google "OK Google" Voice detection / commands even from lock screen. First I would disable the Moto voice feature because I overrides it... Then Open Google Now and scroll down to the bottom and click the options icon on the right the select "setting" then "Voice" .... and finally "OK Google Detection" Here you will see the options for setting it up as well as the option to have it active when screen on, and even when from secure lock screen, although I'm not positive if screen has to be on at lock screen or not, but I believe it does not.
I use Nova Launcher and with that you can set it to respond even when screen is locked and off. I do believe this should work the same way though. Hope that helps.... Matt