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 Time Tracker for Salesforce application on the device.
Once you are logged in to the app, you can Check-In and Check-Out for 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. Once you are on a proper data connection, the Check-Ins and Check-Outs made when offline gets saved in Salesforce and shown in the TT Details tab.