Yes, ArcMap displays the first 1000 features, but as you pan, it will make further requests for additional features, while caching the first set. In ArcGIS.com, we make up to (I believe) 9 requests for features, because arcgis.com we divide the display area into a grid.
There are a couple of reasons to limit features returned to a client based on how feature services work. Feature services return the actual geometry of a feature to the client, so the client can draw it. So given 1000 polygons, each with 1000 vertices, the amount of data adds up. So we limit it to manage load against the server, but also to manage the amount of data being transferred across the wire to a client. Then, ultimately, the client has to draw the features. Web and mobile apps are much more limited in the number of features they can handle.
Hope this helps explain things.
Mike