To my knowledge, you cannot do this in AGOL viewer, however, you are able to publish your own network analysis services or GP services based on the in-house network dataset and then consume this service in various web applications via REST/SOAP protocol. ArcGIS Viewer for Flex/Silverlight, for instance, are capable of using the mentioned services.
I agree that being able to consume own routing services in ArcGIS.com Viewer would be neat and I guess ArcGIS Online team does work on this and this functionality might come in some later release. You are welcome to publish an idea at ArcGIS Ideas web site.