No. And I doubt if this will change for the free version.
Cloud business has an automatic App update (only for the stream though not the work-space). And at this point only once per day at a set time). But it costs $25 per user per month. But even for this for now the tables (QVDs etc) has to be manually uploaded. But Qlik plan to have automatic uploading of these tables by the first quarter of next year (hopefully this is still the plan).