Yes, your Echo will work anywhere you can access the internet via home broadband router wi-fi.
However, it is possible or even likely that your Audio streaming services license terms & conditions will not make the music catalogue and streaming available beyond the market region in which it was purchased. This has nothing to do with the Echo or the Alexa service. It is defined in the relationship between you and your audio streaming service.
Other skills and services may also be limited by geographical region.