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 PDF document describing ringing 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.
To actually hear some of the most common ringback tones used across the world visit this page: https://en.wikipedia.org/wiki/Ringing_tone.
When running a business or for various other reasons you may not want people dialing your phone number to know that you are in another country. One 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 Voice over IP provider, you likely can redirect calls to your new VoIP number depending on your current service plan. You would of course need a reliable broadband Internet connection at your location abroad.
A second and probably easier to set up solution is using a Call forwarding service. How this one works: you sign up for a plan with one of the companies providing this type of service and they'll give you a toll free or local phone number in a geographic area of your choice. Incoming calls will get forwarded to your real phone number. This type of service is also based on VoIP and you should be able to choose a ringback tone people hear when calling you regardless of where you are located.
Some VoIP/Call forwarding providers: