Are nested try/except blocks in Python a good programming practice?

Your first example is perfectly fine. Even the official Python documentation recommends this style known as EAFP.

Personally, I prefer to avoid nesting when it’s not necessary:

def __getattribute__(self, item):
    try:
        return object.__getattribute__(item)
    except AttributeError:
        pass  # Fallback to dict
    try:
        return self.dict[item]
    except KeyError:
        raise AttributeError("The object doesn't have such attribute") from None

PS. has_key() has been deprecated for a long time in Python 2. Use item in self.dict instead.