If I advertise my website banner on popular website, will my website get crawled by google for search results when the popular website appears in google search I know website text link gets crawled by google when the popular website appears in search results. Is it the same with banners?
As httpwebwitch said, it all depends on how the banner is being served. If the site you run your banner on uses an ad server then they may have all sorts of redirects and click counters that will prevent the search engines from being able to crawl your link.
Search engines will be able to find you via your link if it a plain vanilla html link from the banner image to your page.
You may want to research into this before you sign up for the ads.