No, Google does not send search forms via its crawlers. Our filters also include the "nofollow" attribute by default to prevent Google from doing this in the navigation. Only those search and filter result pages are indexed which are directly linked and therefore relevant for Google.
An exception here is the product listings on the category pages, which are relevant and visible for Google and are therefore indexed as usual. We recommend to send a sitemap with the links to all of your product detail pages to Google - as this is best practice in e-commerce.