Not really, because it is the opposite what likely to happen. Alexa ranks website based on the traffic a website receiving and that’s all.
So, if you receive high traffic through Google search results, you have a good chance of improving your Alexa rank.
It may not be accurate always. Alexa rank websites based on the information they get. It ranks mainly on the number of unique visits, page views, etc.
So we can conclude that Alexa rank doesn’t affect your site from showing on Google search results.
Also, Google ranks a website based on many SEO factors which include Domain Authority, backlinks, content, etc.
Google is a search engine and index every website, rank them based on the relevance, location of the user, etc.
Alexa rank can be used to analyse how established a website is and can help you get the traffic volume the website is receiving.
There are lots of use case of Alexa tool, it includes finding your competitors, search terms your competitors are ranking for, etc.
Let me conclude it saying that Alexa rank doesn’t affect your Google ranking, but vice versa could be possible since if your Google ranking becomes poor, Alexa rank will decrease because of reducing traffic.