No, bttn devices must always have Internet connection and be able to contact the cloud server. The bttn actions are executed by the server and the cloud server controls the bttn's lights and usage rights.

In cases where opening access to your service from the open Internet is not possible, you might be able to use a new feature in Wi-Fi bttns running firmware version March 2016 (201603): Auxiliary HTTP requests

The auxiliary HTTP requests feature allows the bttn device to send direct HTTP GET or POST requests to your service, without going through the cloud server. The bttn will still need to connect to the server, but the server can be configured e.g. to just count pushes. 

For instructions on how to setup the auxiliary http requests, please see the following support article: