Yes, in time non-ADA compliant websites will be penalized in the search engines. It's already on their radar. But for now they are still negatively affected, just in an indirect way. Live traffic behavior (user experience) is now factored into Google's algorithm and is a ranking signal. Negative user interactions absolutely have negative affects on rankings.

The need to make websites, mobile apps, and other online properties accessible to all is only going to increase as time moves on. Smart business owners will do well to get in front of this issue and make sure that their websites are ADA compliant now so that all their customers have the equal access to the resources they offer. Not just because they want to avoid a lawsuit or government action, but because it’s the right thing to do.
If your website is not already ADA compliant, you are automatically missing out on millions of potential customers who cannot access your site due to their disabilities. In fact, there are nearly 50 million people with disabilities in the U.S., which means about 19 percent of this country has a disability. Many of them might be interested in your products or services, but once they arrive at your website, they won't be able to navigate easily enough to buy anything or even contact you, all because your website is only accessible to people without disabilities. Thus, they may move on to your competitors.
This particular lawsuit amounted to nothing more than a shakedown for cash, as the current laws would make it difficult to win the suit in court (more about this later) but it prompted me to dive deeper into the issue of ADA compliance. Through my research, I discovered there are some new laws on the horizon that could make ADA compliance mandatory, which means web designers and digital marketers need to know how to prepare.
The Department is evaluating whether promulgating regulations about the accessibility of Web information and services are necessary and appropriate. Such an evaluation will be informed by an additional review of data and further analysis. The Department will continue to assess whether specific technical standards are necessary and appropriate to assist covered entities with complying with the ADA.
Yes, as of 2018 websites absolutely must be ADA compliant.  Its a new but very scary issue that has flared up over the last year and is set to cause a LOT of turmoil.  The Supreme court issued a judgement that opened up a loophole and opportunity-chasing lawyers are aggressively soliciting handicapped people and convincing them to sue unsuspecting website owners (pretty much every website owner on the planet, as not a single one of us were ADA compliant before now.)

The words in the tag should be more than a description. They should provide a text equivalent of the image. In other words, the tag should include the same meaningful information that other users obtain by looking at the image. In the example of the mayor’s picture, adding an “alt” tag with the words “Photograph of Mayor Jane Smith” provides a meaningful description.
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