Could and should a web server not respond to a unwanted request?

With firewalls, it is possible to put it in a stealth mode meaning that it will not actually deny any incoming traffic with an explicit refusal but rather silently drop the packet, making it harder for malicious users to determine if there is a machine at this location.

In the HTTP protocol, could a server be made to behave similarly? Is it desirable to have such behavior instead of returning 404 (which usually indicates there is indeed a machine serving content.)