If you are in the States, you will need to have a valid medical license in the state you work in. And since as a new grad, you'll have a training license, and cannot work outside your training program under that license, you won't be able to act as an MD/intern legally. (Plus the training license start date will likely be for the day your residency program starts, so you'd be completely unlicensed between graduation and residency). Obviously you could act as a sub-i/student and get things co-signed.
If going abroad, it would depend on the country's laws regarding this type of thing. Some places may not let you do this, depending on the health care environment in that country. I suspect that most third world countries are unlikely to regulate you, but admit I have no specific knowledge to support this. Someone who has done medical mission trips may have better info.