I'm wondering if the SharePoint connector module is deprecated with the new version of Sitecore. I can see a lot of about Sitecore and SP 2007 / 2010. But seems not the case any more with Sitecore 7 and SharePoint 2013.
Is Sitecore now could be used as Document management too?
The latest version of the SharePoint Integration Framework (SPIF) was released on July 18, 2014 and Sitecore states that it was "tested with Sitecore CMS 6.6.0 rev. 140410 (Service Pack 2) and Sitecore CMS 7.2 rev. 140526 (7.2 Update-2)."
You can find more information here on SDN.
Regarding your question of whether Sitecore could be used as a Document management tool, that depends on your requirements. If you can model your Sitecore instance in such a way that supports your requirements, I would say, you can use Sitecore as a "document management" tool. But if you're comparing directly to Sharepoint, I would say "no". Sitecore is a CMS. Sharepoint is a document management tool. The SPIF exists to connect the two so that one does not replace the other.