I don't recall seeing any https pages ranking in the top 5 or even 10 for competitive phrases. One of my friends told me that
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public https pages can definitely be indexed and rank. The Adwords "keyword tool" page is one example, just off the top of my head. In fact, there are many posts here where people complain about seeing the https versions of their urls in the search results when they don't want that.
However, there are also many webmaster experiences that indicate all-https sites do not see their pages crawled as deeply or frequently. When they switch to http protocol they see an increase. So, I assume the slower server response would be a significant factor in lowering the crawl budget.
Using https would not be my first choice in competing on a major keyword, but it's not impossible -- just harder.