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If the GA tracking code is on the website, then it will capture the traffic regardless of whether GA is setup with the http or https version of the site. You might also find this MOZ Question and its answers useful: https://moz.com/community/q/will-changing-the-property-from-http-to-https-in-google-analytics-affect-main-unfiltered-view

And if people don't have Search Console access, they can always try queries like: https://www.google.com/search?q=site%3Abbc.co.uk ... however, due to the difficulty in exporting all the listed URLs, and due to some anti-scraping measures by Google, this data tends to be inferior to that supplied by Search Console. Always use Google's official tools first