Read data from Database within After Effect

You can build your own system with sockets as outlined in the docs

or even easier someone built a fairly simple to use library for making HTTP requests in ExtendScript.

Example Usage:

var data = $http({
method: 'GET',
url: 'http://example.com/data.json',
headers: {'Accept': 'application/json','Content-Type': 'application/json'}
});
alert(data.payload);

Unfortunately HTTPS is not supported FYI. If you need it, you may want to make a CEP panel instead.

It's definitely possible.  You would need to use Sockets to communicate via ExtendScript.  You can also use something like Templater from Dataclay to easily handle this, but you would need to create a small server that you point Templater to rather than a direct connection to the database.  See this support article for more information on how Templater communicates to an endpoint exposed by an API that you implement.