If someone searches on my wordpress site as "XYZ" Will google crawl this search result page ? Is there any wordpress plugin for that in case Google doesn't crawl it by default.
Google will crawl and index any web pages which has contents and have already some links pointing at them.
i think, you need to rephrase your question... and yes google crawls your pages and it has no time boundation. So your visitors from google, doesn't bring crawlers