Personally, I am not an Instagram user; but, I am very much a user of the Internet in general, and yes. If Instragram becomes a very "ad aware" website, it could very push users away from the site. Nobody wants to see ads all over the place, especially pop-ups. If this becomes an issue one day, any user would more then like look else where. There are always competitor websites out there, especially ones like Instagram.
There should be three things of certainty in America: death, taxes and Internet advertising on "free" sites. Just like network television shows, the companies that own Internet sites have to get their money from somewhere. Unless the website is a charity or accepts donations, chances are advertisers are paying for certain Internet sites that are "free." Ads won't ruin Instagram, ads on the Internet are simply a way of life.