ARQ supports HTTP Basic Authentication for read queries (setBasicAuthentication() in QueryEngineHTTP).
I can't find authentication support for SPARQL Update though. The responsible class UpdateProcessRemote uses HttpOp as an abstraction, and HttpOp in turn encapsulates HttpClient from Apache HTTP Components.
So I guess a way to go would be to extend HttpOp to support auth or to expose the HttpClient object in order to set auth options as described in .
I'm happy to help if I can get some hints about the preferred way to include auth support.