Check if searchform is included?
The get_search_form() function (that should be used) uses locate_template('searchform.php'); to display the search form.
The later returns (as you can see from its source)
the template filename if one is located
So if you’re just wanting to catch the default way, then you should simply test
'searchform.php' === locate_template( 'searchform.php' ) AND print 'Search form displayed!';
You can maybe think of a hundred of other scenarios on how to include the search form, but you’ll never catch them all.
The real problem (and I don’t have a solution for that) is that this only checks the existence, not if it is included via a widget. So above is only meant to work from inside a (custom) widget.
Display widget programmatically
If you want to display a widget (in absence of others) via PHP code in your template, then go with the_widget() Source link.
Check your sidebars
To inspect your sidebars, you can simply check the $GLOBALS['wp_registered_sidebars'].
Check your widgets
Core also has a possibility to check the registered widgets: wp_get_sidebars_widgets(), which you can use to check for the existance of a widget.