Can the apple watch call emergency services without the person initiating a call, like when a person falls unconscious.

Read this page;

Use fall detection with Apple Watch

marlenb11 wrote:

How can you press a button if you are unconscious? If the watch detects a fall and the person takes no action with the watch because the fall rendered the person unconscious will the watch call emergency services?

Follow the link fieryjack has provided

yes, just press the side button until the emergency sos slider appears