WordPress conditional functions will not tell you which template file is used. They tell you what the current request is for. Which file is loaded for that type of request is determined by the template hierarchy.
So, is_search() will tell you if search.php is being used if the current request is a search, and the current theme includes a search.php. If the theme does not include search.php, is_search() will still return true if index.php is used, as per the template hierarchy.
That’s the long way of saying that if your theme has search.php, then yes, use is_search().