Well the nice thing about push notifications is they are very easy to turn on and off, and apps that feature them universally allow you to choose whether to activate them or not as soon as you download them.
And I agree that an app could an excellent way to expand recognition of the game. However, I'm guessing that one would not be easy to develop. Smart phones these days tend to be icon-based, and don't rely as much on text, and are not particularly friendly to text-based interfaces for that matter. We'd also have to have a mobile interface for registering for the game.
And I would say that there's no need to develop one for every mobile OS under the sun. Do one for Apple (which is much more standardized hardware-wise than, say, Android) or really whichever we can get someone to volunteer to do, and leave it at that.
The actual app would be relatively easy, making sure it played nice with the existing server might be more difficult, I've never tried making an app that would access a server via standard URL strings, and I doubt anyone wants to spend the time creating a mobile interface API for the server
