As we talked to users of GraphQL, we realized that there's a lot of value in building a production-ready GraphQL client that's easy to use and simplifies using a GraphQL backend for a production app. Since we've realized that, we've focused our efforts on building Apollo Client to satisfy those needs by providing a straightforward API and features such as query batching. So, although Apollo Client has been built with reactivity and server-side push in mind, it is not at the very top of our priority list.
That said, we do already provide some degree of reactivity. If your application uses a view layer such as react-apollo or angular2-apollo, mutations that modify data and queries that fetch new data will automatically update your UI. Also, if you using polling queries, your UI will be updated as new data comes in. As an example of this in production, we actually reimplemented the Meteor Galaxy UI to use Apollo and it renders a live, reactive dashboard with container metrics, an activity feed, etc. using polling queries. Through query batching and scheduled polling queries, this approach can be performant enough to use in many situations.
Although we don't yet have an implementation of server-side push over WebSockets, we are working on implementing it in conjunction with GraphQL subscriptions and would be happy to work with others that are interested in getting this done.