Yes, you can track time without a data connection.

You will need a Wi-Fi or Mobile data connection when you log in to the PK4 TimeTracker Mobile app, on the device.

Once you are logged in to the app, you can Check-In and Check-Out of a Job or Project without a Wi-Fi or Data connection.

The Check-Ins and Check-Outs made on the device when offline, get saved on the device. When the device is connected with a proper data connection, the Check-Ins and Check-Outs made when offline get pushed to Salesforce and are shown in the TT Details tab.