Can I use our web server to replace Dropbox?

No. A web site is not meant for file sharing within your organization unless it is done through the files module in Tendenci.

If you must do use your site like dropbox because someone in management remembers the old days of FTP and thinks it's still a good idea (it's not), please consider self hosting the Open Source version of Tendenci.

But really, you don't want to do this. Use a file sharing service for file sharing and keep your web application server isolated, hosted with us or somewhere else. Your web site is just too important to have one person with an infected PC take out your entire web presence.