Google’s John Mueller said it would be “extremely rare that Googlebot would submit a form” on your web site. He said Google did this more often in the old days, espesially on governmental web sites where there was no site navigation and the only way to get to public content was to use a search box on the site. But nowadays most sites have good navigation through links and it is is rare for Google to have to submit forms.
He added that if you do see GoogleBot submitting forms on your site, it might show that you need to improve your site’s navigation and architecture to enable Google to crawl the site normally.
He said this at the 15:08 mark into this video:
Here is the transcript:
In 2008, Google said it can crawl content behind forms but as soon as 2015 Google said this was only done if it cannot access your content via normal navigation.
Forum discussion at YouTube Community.