No. It doesn’t. ClickOnce only supports proxy authentication using the default credentials, i.e. Windows Integrated Security, i.e. the Windows account information.
System.Net's default web proxy has [UseDefaultCredentials] turned off by default. You'll probably have to turn this on by modifying the machine.config file. If the ClickOnce deployment itself does not require a proxy server, but the application does, you
can add an entry to the app.config file instead.
If the <defaultProxy> element in the machine.config is empty, it uses the settings from IE -- but this applies to calling something via a proxy server, not to installing the ClickOnce app itself.