I confirm we can not download the app through Google Play. It also does not work for my device (Android Nexus 5) in Shanghai due to the connectivity with Google Maps. It is a pain I must say, but most people find workaround.
Are you sure about the second point? I use Uber on a Nexus 5 and it works fine in Shanghai, without requiring VPN. IIRC Uber now uses Baidu maps in China.