Is it possible to use ESP8266 modules interchangeably?
yes they are interchangeable since they all use the same chip (esp 8266). However the pin outs of the different modules can (and will be) laid out different. So you have to watch out that your wires are connected to the correct pads on the module.

Also mind that different esp8266 modules can be (stock) loaded with different firmware. If you are using the AT firmware in your current arduino project it can be necessary to flash your new esp8266 module with the same firmware. If you are not sure how to do this you might have a look to the esp8266 forum