I guess with 'header position' you mean the module position.

The way Conditional Content works, is that you surround the content you want to show/hide with the plugin tags {show}/{hide}...
There is no way to surround a module position like that. So no.

If you don't want the header position to show, just don't place any modules in there.
Or if you want to conditionally show the module(s) in that position, you can use Advanced Module Manager to control those modules.