In short, no, neither of your two alternatives is “possible” in the sense of able or at all likely to do what you seem to want it to do.
There is no get_header filter – so the first alternative won’t do anything.
The second one might do something, depending on what your function contained, but isn’t how this is done.
There is a get_header action hook whose use is described in the Codex here: https://codex.wordpress.org/Plugin_API/Action_Reference/get_header
It does allow you to narrow its scope by name of specific header file. Depending on what exactly you want to happen when it fires, it might be one way to achieve whatever it is you want to achieve.
Since there are no specific get_header filters, the main ways to modify your header are either to create one or more new header.php or header-{name}.php template files for your child-theme (you can have multiple ones for templates to choose from).
If you want to change specific elements in your theme’s header without hacking it or creating a new header(-name).php file, you can use one of the filters you can find in wp-includes/theme.php. https://core.trac.wordpress.org/browser/tags/4.5.3/src/wp-includes/theme.php#L0
Determining which alternative or alternatives you need will depend on what “fragments” you need to modify.