I set it up locally. It works very well :)

After investigation, I don't see any blocker for us.
The QuickSurveys extension is very autonomous, you just need to configure the survey in LocalSettings and create the necessary wiki pages for the question and answers.

array(
    'name' => 'search-satisfaction',
    'type' => 'internal',
    "question" => "survey-search-satisfaction-question",

    "answers" => array(
        "survey-search-satisfaction-yes",
        "survey-search-satisfaction-moderate",
        "survey-search-satisfaction-no",
    ),
    "description" => "survey-search-satisfaction-description",
    "enabled" => true,
    "coverage" => 0.5,
    "platform" => array(
        "desktop" => array( "stable", "beta", "alpha" ),
        "mobile" => array( "stable", "beta", "alpha" ),
    ),
),
// Note that these params have to be refined, 
// this is just for me to test that it works :)

Based on that (and thanks to the work already done for the search satisfaction event logging), it is very easy for us to append the query string parameter to the URL &quicksurvey=internal-survey-search-satisfaction when the user comes from the search results page.

I'm adding a screenshot, but the question and answers are again just for me to test that it works :) They have to be refined of course.