Unfortunately, there is no 100% guaranteed answer here. Google keeps its search engine ranking algorithm secret for a very good reason. If people know what Google checks, they will artificially inflate this statistic and unnaturally boost a website. When it comes to how Alexa affects search engine results, it is unlikely, but a good rank usually means your site is doing well and here's why.
Traffic on your website is a good signal of a good website. If a site has 1 million daily visitors and another has 10 visitors, it is safe to assume that the site that is getting 1 million visitors, is better and more popular. Google monitors this kind of thing and will, of course, make the most popular site rank higher than the site that is less popular. Alexa rank will reflect this popularity and is great for you and other humans to see how popular your site is. Google is capable of tracking traffic on its own, so it is unlikely that it uses Alexa to influence its results, but that doesn't mean you shouldn't be wanting to get a good Alexa score for your website.
Humans are the ones that use Alexa. Marketing and advertisers will often check this site to see how popular your website actually is. If your site scores well, it will be seen as a valuable site and people will approach you to advertise their products on your website. This is almost as valuable as good SEO as it will give you a solid source of income for your website. So the question that might come from this is, how do you increase traffic to your website without SEO?
Getting traffic to your site can be difficult when you have a new website. You need the traffic to get good SEO ranking, but it's hard to get traffic when your site isn't showing up in search engine results. It's the catch 22 that ever website owner is going to deal with. Buying reliable traffic is a solution to this, but there are a lot of sources that send robots to your site which don't help at all. They offer affordable traffic that really boosts your website's online presence. For those who are looking to get a boost in traffic while you are working to increase your SEO and online presence, this can be a valuable source for you.
So to get back to the original question, does Alexa boost SEO? The answer is no, but it is a great way to check if your SEO efforts are working. A good Alexa rank will usually indicate good website SEO and performance.