I don't get an alert outside of the game whether or not an event or someone in-game messaged me. It would be really nice if I could enable Push notifications for the game. For instance, if a club event was going to start soon I could get an alert on my phone that says so, I think this can encourage club activity more if people offline are reminded of it. It really sucks when there's only a handful of club members participating in an event. (I wonder if that's more of a club member issue though)
However, if this is impossible because of technical issues, I understand.
For instance, I have all the available character slots taken up with different class characters, and it would be bothersome if notifications for each of those characters kept alerting me. One account at a time would be nice.