You should be able to do that if you have a wifi connection. International data rates are typicallly much higher than the US, and much higher than international voice roaming.
Options:
1) try and get a local SIM & unlocked phone. If you're using the DeathStar (ATT) network, I understand that unlocking an iPhone is not an option (but I'd still ask). That leaves you with the option of getting a cheap unlocked phone (voice only) or using another option. (
Link to Telestial
2) I don't recall whether SkypeIn will send an email with attachment or not. I know Ooma will ('cause I use it...), GoogleVoice will (remembering that there's limited privacy there), and some of the other services will. Simply have folks leave a message & you call 'em right back on a cheap VoIP connection.
EDIT:I found this on a website about Belize:
VOIP is blocked in Belize and will remain so for the foreseeable future as the government controlled Public Utilities Commission believes it would reduce profits for the telephone companies.
That would effectively prevent use of Skype, Ooma, or any other VoIP service (unless you use a VPN system to bypass the local controls). Forces you to another option.
3) Get an international roaming SIM card from someone like Telestial. No, not the cheapest solution, but in some countries incoming calls are free. It's still vastly cheaper than roaming with a US number. Again, you'll need an unlocked phone to take advantage of this.
Money-wise, it comes down to this: if you can't get your phone unlocked, buying an unlocked phone is not worth the money unless: 1) you're planning to travel a lot overseas, 2) you're going to be there long enough to pay for the phone in savings, or 3) you're going to make enough calls to make up the cost of the phone in savings w/a local SIM. Fortunately, older generation voice-only cellphones are pretty cheap to buy unlocked......