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. SharePoint 2013 supports (out-of-the-box) windows (i.e. NTLM), forms-based, and SAML-based claims authentication..
If you'reyour SharePoint WebApplication is configured to use windows authentication, wget NTLM should work. As should the curl --ntlm
-command.
If you'reyour 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 for ideas on how to do this.
I have no idea, what you could do if the SharePoint is configured for SAML-based claims authentication.