Yes, probably hundreds of thousands of people have done this. They all chose one of the client implementations on the "ACME Client Implementations" page that I linked to above, installed it on a computer, and used it to obtain certificates.
If they didn't have administrative access to their web servers, or they installed the client application on a machine other than the web server where the certificate was used, most of them have probably been annoyed by the renewal process and concluded that Let's Encrypt is such a great service—largely because they weren't using it as intended.