This depends on the configured authentication-method. 
I.e. your method of access needs to be the same. 

wget IMHO supports [basic, disgest and NTML authentication][1]. SharePoint 2013 supports (out-of-the-box) windows (i.e. NTLM), forms-based, and SAML-based claims authentication..

If you're SharePoint WebApplication is configured to use **windows authentication**, wget NTLM should work. As should the `curl --ntlm`-command.

If you're SharePoint is configured for **forms-based authentication**, you'll need to fake a login, and pass a cookie in your download-request. Check [this question][2] for ideas on how to do this.

I have no idea, what you could do if the SharePoint is configured for **[SAML-based][3] claims authentication**.


  [1]: https://www.gnu.org/software/wget/manual/html_node/HTTP-Options.html
  [2]: http://stackoverflow.com/questions/1324421/how-to-get-past-the-login-page-with-wget
  [3]: https://technet.microsoft.com/en-us/library/hh305235.aspx