It should be possible. But I think you’d need to write your own short code function. Also, you’d have to make sure that acf_form_head(); is called before get_header(); in every template where a form could possible be added, alternately you could put the function call in header.php before any HTML output. I think the inclusion of the acf_form_head() function call is probably why ACF does not have a shortcode for adding front end forms.
There are other form plugins that can be used and you could create your own forms. The thing you need to make sure of when updating data yourself is to make sure that the field_key entry in postmeta is also created. More info on field_key and database entries can be found on this page http://www.advancedcustomfields.com/resources/get_field_object/
I’m pretty sure that some form plugins like Gavity Forms have add ons for ACF, don’t know about Formidable.
