Yes AND No.
You can go here to learn more about SEO.
http://www.etsy.com/teams/11352/relevancy-and-seo-for-all-etsy-shopsAfter I tweaked my shop -SEO- after having it open earlier this year, I noticed that some of my listings would show up in page 3, 4 or 5 in popular searches instead of page 1 or 2.
I did some more research and yes, other shops on page 1, with similar items, had more views, hearts, and were in more treasuries than mine. I had my shop critiqued AGAIN, which I knew that they couldn't really tell me anything more about titles or keywords because I was already RELEVANT in searches on ETSY and Google, so, what else could they tell me? Well, I learned that those shops on page 1 had more views, hearts and were in more treasuries than mine therefore, they will turn up higher in searches than my listings.
If you have not tweaked your shop for SEO, relevancy, etc, having more hearts wouldn't really have your shop show up higher in search results.