You can, but you have to go through Google Music on your phone. I suggest making a playlist first that way you can shuffle all your music instead of just one album on your watch. Basically launch Google Music from your phone, select your playlist or an album and hit download. So it will download so you can play that music offline. Then go to Settings, scroll down and check Allow for Android Wear (or something like that). Once the music is done downloading on your phone, it will automatically start downloading to Android Wear.
It takes a long time to download to the watch depending on how much music. I did like 200+ songs and it took hours. I basically left the watch on the charger and sat the phone by it while everything loaded. But after it's done you can basically listen to the music on the watch without being connected to your phone. You just need bluetooth headphones synced to your watch as well. On the watch, if you go to start, you'll see Google Music. Sorry for the long explanation, but hope that helps. I've been just wearing my watch at the gym and playing music that way. Very convenient. Does drain battery quite a bit.