I'm not involved in Architect directly, but I built iOS and Android packager for Sencha Touch 2.0, which is part of Architect. But no, it does not support SQLite just yet, however it will support it quite soon I suppose. At the moment there are only: Connection, Notification, Orientation and Camera classes, all written in NK 2.0 API style, here is the doc: http://docs.sencha.com/touch/2-0/#!/guide/native_apis
to give you idea how NK 2.0 APIs will look like.
Also from now on all NK 2.0 APIs will work on both iOS and Android