I haven't heard of a message telling folks that you're out of the country being in the automated system. Are folks calling you and mentioning hearing a message?
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No, not answering will end up in the same place but they may hear an odd foreign double ring before the transfer to VM. You do know that not answering an incoming call while roaming abroad will result in a roaming charge to your account? I normally forward all calls to voicemail, listen to the message using Visual Voicemail and decide if I want to call the person back right away, send a text or wait until I'm on WiFi.
If you are using a different SIM card, you will more than likely have your T-Mobile SIM card out of the phone and calls to your US number will just go straight to voicemail. You can change your voicemail greeting and let them know you are out of the country and give them your new international number (they will be changed for calling that though) or you can let them know to message you on social media if you use it instead.