As a web application, nothing within the Analyzer is directly related to the TLS. However, please check the SQL Native Client on the webserver to see if it is up-to-date with TLS 1.2. Here is the download link.
The Microsoft website has more information on which SQL Server supports TLS 1.2.
Since enabling TLS1.2 makes no difference to the Analyzer software as it is similar to enabling the SSL which is on a higher level. According to a Microsoft article, you will have to update the .NET Framework, native clients, etc. before you switch on the TLS.