I've been using Chrome to Phone pretty much every day for the past couple of years, for this and other stuff. You look up a route, click the button, the link is sent to your phone, you click on it, it opens up in Maps. Then it works the same as if you manually enter the route query on your mobile device.

I'm not sure how the could integrate it more (or even less) with Maps or Android or what the phone being off or locked has got to do with it. It syncs the same way all Google services do. I suppose it may be working less well on an older or oddly (manufacturer) customized device.