So, in addition to what I posted above, I verified that no, GW doesn't show up in My Apps when I go through Play on the phone. However, if I go through my phone using the browser method originally used to get GW installed, it shows that it's compatible (in browser) and installed (in Play). Also, I have automatic updates checked.
While I can't see it in My Apps, an in-app check (settings->about) shows the same version number (1.1-R57v5) as the April 13 update on the market.
So it seems that if you can use the browser method to get to the app in the market and set it to automatically update, it will stay up to date with the latest version.