I only want to confirm this because recently I found a page in my website in Google SERP that is only accessible when a user is logged in. The link to this page is also only available when the user is logged in. Therefore, the Google search engine bot has no way to crawl this page because technically the bot is only a "guest" to my website. In this page for logged in members, there are google adsense displayed. So I assume that adsense is also being used to index a page. Is the assumption true?
No, the mediapartners bot will come because adsense calls it to determine what ads to show. However, it won't be able to see the page if it's not open for guests.
That's true; from what I've heard, all of the URLs that are crawled (your page crawled by the AdSense bot) are put into one big "pot" and those URLs are then shared with all the other Google bots. Keep in mind that if you visited the page or someone visited that page and had the Google Toolbar installed they might have gotten the URL that way, as well.