The short answer is yes.
Even without a Wi-Fi connection, your ecobee will still function as a traditional thermostat; it will engage your equipment as needed and maintain your comfort set points.
You can simply skip the Wi-Fi Configuration portion when setting up your ecobee, though please be advised that skipping this step and never connecting your ecobee to Wi-Fi will not allow you to complete the registration process, so you will be unable to create an ecobee account.
In the event that you require assistance from our Support team, without a registered ecobee account with sufficient data, our Support team will be quite limited in the assistance they can provide, so we recommend initially connecting to Wi-Fi to at least register your thermostat.
After you've registered your thermostat, if you choose to proceed without a Wi-Fi connection, you will lose some of the ecobee's most useful features such as:
Remote access through the mobile app and Web Portal
You will not be to check the status of your thermostat or make any changes through the mobile app or Web Portal.
Your thermostat will not have access to any weather data. If your home has a heat pump system, the ecobee relies on weather data to determine if it's safe to run your compressor.
To generate Home IQ and System Monitor reports, your thermostat needs to be online and communicating with our servers, so you will not receive any efficiency reports or have access to any runtime data.
HomeKit, Alexa, and other APIs
Since HomeKit (Siri) and Alexa require a stable Wi-Fi connection (as do all other apps such as IFTTT, Wink, SmartThings), you will not be able to utilize any of these features.