iPhone 4 operates only with WiFi connectivity abroad
In short, yes, it should perform normally for you even when you don't have data enabled.

Your iPhone 4 can connect to a Wi-Fi network whenever Wi-Fi is turned on and there is a Wi-Fi network within the range of your device. Wi-Fi connectivity is independent from Cellular connectivity. You can turn Wi-Fi ON or OFF (in Settings.app -> Wifi) and you can also turn Cellular ON or OFF (Settings.app -> General -> Cellular -> Cellular Data) independently. 

If you are internationally abroad and you want to keep your device from connecting to a Cellular network, turn off "Data Roaming" in Settings -> General -> Cellular.