Can Truecaller Android get Caller ID on 2G connection?
People install Truecaller app. 
The app uploads all your contacts name, mobile number, photo and other details to its server. 
The app queries its server with the number which is calling you and gets persons name and displays it.
So you see Truecaller needs internet access to function whether through the Wifi / GSM/GPRS/EDGE etc. network. So you are in a location with only 2G and no Wifi, Truecaller cannot get a CallerID.