Short answer: very likely. Countries often do not use the same sound frequency and cadence for the sounds we hear when dialing a phone number: ringback tone, busy tone, and so on.
The International Telecommunication Union publishes a list of tones used by national networks across the world. To compare ringback tones between different countries look at the sound frequency and cadence they use for their various types of tones. For example, the US uses the familiar 2 second ring followed by a 4 second pause while, when dialing UK phone numbers you will hear a double ring followed by a 2 second pause.
When running a business or for various other reasons you may not want people who call your phone number to know that you are located in another country. The only workaround that comes to mind in this case is using a location independent cloud phone service based on Voice over IP technology (VoIP). There are a plethora of companies providing these types of services, many with a relatively long history in the business. Usually they have plans designed for both individual and business use, with useful features available, including customizable ringback tones. If you want to keep your current phone number but do not want to port it to a new provider, you likely can redirect calls to one of these virtual numbers. You would of course need a reliable broadband Internet connection at your location abroad.
Some Internet phone service providers: