Document Connector has no delete from SkyDrive (at least not for SkyDrive Pro connection), no sharing functionality, no local copy of files unless you download them (equals no internet, no access).
I have also found it to be incredibly unreliable in retaining the connection. I regularly get 'SkyDrive Pro is no longer available' messages and then need to restore the connection by copy and pasting the web address for the Doc Library.
The limitations of delete and share, make the website more functional and considering that I have to download the files to have them locally, I would rather use the web interface.
Based on the above limitations and a few other minor ones, I don't view Document Connector as a solution to this question.