Not really, but perhaps you using the wrong terms:
A shortcode is a manually entered piece of text where code has been programmatically added so that when wp runs ‘the_content’ filter , it’ll then call the function and replace the piece of text with the returned result of the function. It’s a specialised form of a filter.
It sounds like what you want is that you’ll need to know the actual function to call to get the text you want, ie the function that the shortcode calls, then write a filter that uses that function where the filter runs on the piece of html that you want to modify:
1) a filter on the title:
There is an example here on using the ‘the_title’ filter https://developer.wordpress.org/plugins/hooks/filters/
or
2) Or on ‘the_content’, where you could call the function that creates the text you wand, add it to the front of the content, and return the result?
https://developer.wordpress.org/reference/hooks/the_content/
Lots more filters here: https://codex.wordpress.org/Plugin_API/Filter_Reference
The above advice if implemented in a small plugin will work across any themes. If you just want it to work on one theme, you could create child theme (to avoid losing your changes if there is an update to the parent theme). In the child theme, you’d just modify the part of the template (maybe the header? or the post?) where you want to insert text.